Preamp gain ???

For many people the issue is too much gain, resulting in operating the pre w near max attenuation and at the lower end of the volume control's range. Under these conditions you may be in that portion of the attenuator where channel matching is not v. good and, particularly in the case of a stepped attenuator, where the "steps" are too coarse to give you good level control. Step x, too soft, step x+1 too loud. typically, the perceived volume difference between steps is less as you go to less and less attenuation (higher spls). Not knowing much at all about the technical side of electronics/circuits, I am guessing that this is due to the logarithmic relationship between power output and spls- Need 10x the power (wattage) to sound 2x as loud. So it really does NOT matter much as long as you are able to operate in the middle of the controls range. Believe me, I had a CAT SL-1 w stepped attenuator and 2 clicks up from 0 was too soft and 3 clicks up was "kick out the jams"! A real PITA.

And Charles1dad summarizes all of the issues perfectly on either side of the pre-amp. They all contribute to the "problem" of excess gain which manifests itself in having to operate the attenuator in a non-optimal part of its range. The pre-amp is also the place where you can (usually) have the manufacturer easily resolve the "problem". You can easily experiment w low cost line attenuators at the amp's input to determine how much the pre-amp gain needs to be reduced or use one the better 10 dB attenuators like the Rothwell for a slightly more expensive, easily reversible fix. If you do that and use heavy cables, make sure you provide some support under the attenuator or else, IME, you are likely to have a failure of one of the jacks.

Paperw*- Nothing that you have said is incorrect but you have neglected the attenuation/gain (if active) provided by the pre-amp, which then is added to the gain of the amp. That can result in excessive overall system gain which results in the user having to operate his pre-amp w excessive attenuation which can have negative effects on the sound. The speaker/amp interface is not usually a decision based on max gain provided by the amp vs. speaker sensitivity, and room size, source output and volume preference all vary. Therefore, god in her infinite wisdom invented the pre-amplifier. Some have adjustable gain for each input. Some do not. Some are passive and provide attenuation only. some are active and have varying amounts of gain. Some of have stepped attenuators and some do not. Some have tape loops and some do not. Some have line and phono stages. some of those w phono stages can accommodate LO MC carts, some only MM or MI carts. Not all line level sources have the same output voltage (some CD players can deliver 2V!) The ability to alter the overall gain/attentuation of a pre-amp may be vital under some circumstances. IN fact some manufacturers have recognized this by incorporating separate gain controls via front or rear panel toggle switches (e.g., Supratek); front panel rotary controls (e.g., Joule), internal dip switches/jumpers (e.g., Nagra) or internal resistors that are designed to be switched out or bypassed (some ARC).

I for one cannot imagine that sensitivity would be the primary criterion I would use to pick a speaker. Of course, that does not mean that you don't need to make sure that you don't get a serious mismatch between speaker and amp but I don't think that you are going to go w a 84 db/w/m speaker instead of a 92 dB/w/m just to provide proper volume control.

Again, this also assumes that you have a reasonable match btwn amp and pre-amp based on impedance and input sensitivity. Just my opinion; worth the proverbial $0.02. IME, YMMV, do not try at home, professional driver on closed course, LSMFT, etc, etc. ;~)

if your integrated has pre out and main in jacks or a tape/processor loop, you could insert attenuators in the loop.

Rothwell sells well regarded 10 dB attenuators in RCA and xlr termination.