What is the advantage of being able to select the MONO button?

If you are starting with a mono recording and a mono cartridge, use will only need one channel of the preamp and a mono amp with one speaker. But if you are playing through a stereo amp and two speakers it gets a little more complicated.  For that setup I would put a Y connector on your turntable output to run both channels of the preamp and stereo amp.

The Mono switch is not needed because you are only sending mono from the cartridge. 

I still do not understand why combining "strapping" the signal in the cartridge is any different than combining them in the phono-pre or combining them externally with a Y adapter.

Unlike adapting a stereo cartridge for mono either through rotation of coils, or summing of channels (perhaps to reduce manufacturing cost?) and sold as a mono cartridge, a true mono cartridge only using a single coil (2 leads) and "strapped" to two sets of output pins (so ​​it can be connected to a typical tonearm with 4 leads).

Simply put,

Some so-called mono cartridge strapping two channel together internally in order to output mono signal.

A true mono cartridge strapping mono signal output into two identical channels.

If modern mono records have the same signal on both sides can’t you simply play them on a stereo cartridge with the end result being mono sound?

Yes, but there’s a drawback.

Is there any reason for one to use a mono cartridge on a modern mono record?

The biggest benefit of a dedicated true mono cart is that it doesn’t pick up noise from vertical motion, which a stereo cart can’t eliminate.

Am I wasting my time and money pursuing this?

It depends on how many mono records you own, how often you play them, and whether you can tolerate a little more noise.

You do not need a mono cartridge or mono switch . Mono reissues are cut on stereo cutter heads in 99% of cases so you don’t need a mono cartridge for them. They’ll play fine with a stereo cart. If you have original mono pressings recorded 60 years ago that is a different story!

You don’t “need” a mono button to play mono records.  Whether or not playing a mono record using information from the sum of two identical channels vs. just one channel is a different matter (I have no idea).  You need to sum two stereo channels to play stereo records in a mono set up.  Not everyone who has a mono setup only listens to mono recordings in such systems.

A true mono cartridge has on one signal generating element that responds only to side to side movement of the stylus and ignores vertical movement (which is information in stereo but just noise in mono).  Modern mono cartridges have suspensions that allow for vertical movement of the cantilever even if such movement does not generate a signal because this acts like springs and shocks on a car—it allows the cartridge to better track vertical movements from warps and other bumps and reduces stress on the stylus and cantilever from such movement.

I still do not understand why combining "strapping" the signal in the cartridge is any different than combining them in the phono-pre or combining them externally with a Y adapter. From the descriptions, it seems they are all doing the same thing but at different points of the signal route. And why would any of these methodologies be required with a mono record and cartridge? It seems to me that the signal would be mono anyway. Why do we need to combine identical signals?

If modern mono records have the same signal on both sides can't you simply play them on a stereo cartridge with the end result being mono sound? Is there any reason for one to use a mono cartridge on a modern mono record? Am I wasting my time and money pursuing this?

So, if I understand this correctly, a mono button, y adapter, and "strapped" construction all do the very same thing: sum both sides of the cartridge together so that the same signal comes from both speakers. Correct?

Yes, the reverse-connected Y adapter and mono button combine the left and right channels, but the internally "strapped" construction cartridge is another story.

But why would a mono record not have the same signal on both sides to begin with? It's not made like a stereo record with a different signal on each side.

Most modern record pressing plants no longer have separate machines for cutting mono and stereo records, so most mono records produced after the mid-1960s have the left and right channels cut with identical content on a stereo cutter.

Is the Quintet a "true mono" device? What exactly does this term refer to?

According to Ortofon, the Quintet Mono is a "true mono" cartridge that generates voltage through horizontal movement only, as opposed to stereo cartridges which produce voltage through both vertical and horizontal movement. It "strapped" the left and right output pins together with a horizontal movement coil.

Is this cartridge safe to use on recent releases or just old records? Someone advised that the stylus shape is not correct for new releases and could prematurely wear them out.

The Ortofon Quintet Mono cartridge is fitted with a nude elliptical r/R 8/18μm stylus, which to my knowledge should be safe for use on recent mono releases.

So, if I understand this correctly, a mono button, y adapter, and "strapped" construction all do the very same thing: sum both sides of the cartridge together so that the same signal comes from both speakers. Correct? But why would a mono record not have the same signal on both sides to begin with? It's not made like a stereo record with a different signal on each side. 

Is the Quintet a "true mono" device? What exactly does this term refer to?

Is this cartridge safe to use on recent releases or just old records? Someone advised that the stylus shape is not correct for new releases and could prematurely wear them out.

The mono button does what the Y connector does to sum left and right.  You can then use the amp to feed identical summed signal to the two speakers of a stereo system or use one channel to feed a single speaker.  But, as I opined above, summing with a Y connector or a mono button is inferior to using a transformer to sum to mono.  You can google about the specifics of using a transformer for doing mono.  
 

I don’t have/want a mono system but I’ve heard many that are quite good.  Some mono systems were installed for practical reasons—e.g., a kitchen system where a listener can be in many different locations and still hear all of the music.  

I have assembled a dedicated mono rig (VPI Super Scoutmaster Special Edition w JMW Memorial tonearm, Ortofon Quintet mono cart into Plinius P-100 phono-pre with no mono button). I believe this to be described as a true mono cart and I’m getting different ideas as to what that means. Does this cart require a pre with mono button or is that just for playing mono records on a stereo rig?

According to the manufacturer:

Quintet Mono uses a strapped output to deliver the same output signal from both sets of pole pins. This effectively eliminates the need for mono-specific equipment, making it possible to enjoy true mono reproduction on any stereo playback system.

You don’t need a preamp with a "mono" button, it will play in mono through any stereo equipment and both speakers will output the same content.

What exactly does this button do if I had a preamp that had one?

The function of the "Mono" button in the preamp is to sum the left and right stereo signals into a mono signal for the speaker, so both speakers will output the same content.

What is all this about Y adapters? Do I need anything like this to optimize this set up?

No, I do not recommend using a Y adapter for the preamp output, it shorts the two outputs together and may damage the preamp.

Thanks, but none of that addressed my concerns. 

Anyone?

I used to play chess with my former next-door-neighbor. I'd set up a "chess table" sideways in front of my stereo. I'd set the system to mono so we could each hear all of the music instead of just what was coming out of the speaker we were next to.

There are also issues with how sounds cancel coming from 2 speakers vs. 1 due to head related effects.  The ideal playback for mono recordings really is just 1 speaker, or two speakers right next to each other.

Ideally, one would listen to records mixed and mastered as mono recordings on a mono setup and stereo recordings on a stereo set up.  Listening to mono recordings through two speakers of a stereo setup can sound very good too.  When  listening to stereo recordings in a mono setup with just one speaker, the two channels have to be summed to one.  This is not ideal because a recording engineer would never simply sum stereo channels to do a mono mix.  Still, that is what has to be done so it is best to do it correctly.  A local shop which builds and sells some mono horn speaker systems also builds and sells a box with one or two transformers for doing the summing.  This sounds MUCH better than a Y connector or.  Their tech made a box that held a selection of different transformers and a Y connection so one could do a quick A-B comparison.  There were easily discernible differences, and to me, there were good modern and vintage transformer alternatives (the Y connection was way behind in my opinion).