Is there an ideal (ish) cartridge output?


I just got done building the Pearl 2 and I went back and forth with gain and impedance. Using a cart that had .15mv and another at .3mv. I also have a Sony TA-5650 V-FET that has a vfet MM phono stage that I have been curious to try out. In that curiosity, I read the specs on the phono stage and its 70db SNR, which is meh. I then thought about SNR, THD, gain, and output of phono cartridges and stages. I looked at a lot of specs of cartridges and stages over the years, and as the gain of the stage goes up, the SNR goes down, which eventually leads me to this question:

Is the ideal cartridge output 1.5-2mv? Do you then get a medium output that is the best middle ground for SNR and THD? If that could be the case (or if not if you disagree) then why isn't there more cartridges with around that output available? 
enobenetto
While I would agree that low moving mass is a desired quality in a cartridge, it cannot be the whole story. And if low moving mass per se is the major goal, then there are moving iron, induced magnet, and other types that inherently have lower moving mass than any moving coil cartridge. This subject comes up at least once every six months, if not even more often.
low moving mass of air core is preferable side effect - air core IMO works better as magnetic field is more homogeneous so sound is more fluent/real. 
Interesting insights from all. Lewm, has heard this before, so I will search for more of his posts, there could be a lot of info I can find out. The low moving mass part of this discussion I have read about before. I would like to try an air-core cartridge when money permits. It seems that Lyra cartridges have a good compromise of all that has been discussed, maybe that is why they are so popular? Although, the sound is the sound, and if you don't like it, than it doesn't matter how it's made. 
Dear Lew, Is your praise of ''your'' Ortofon MC 2000 not in
contradiction with your statement about ''output''? As far
as I know this cart has the lowest output ever(?) 0,05 mV.
Besides still one of the ''best ever'' despite its age. 
There is a quality of sound that I look for when determining what the ideal output of a phono cartridge is that is a little more ephemeral. This observation is based only on my experience with my chosen components over the years and may not apply to anyone else, but I have churned enough cartridges and phono stages over the years to believe there is something to this.

We all know that most preamps sound best with the volume control fairly wide open; iow, as little attenuation of the phono stage’s signal as possible. Obviously, the overall gain structure of a given system dictates what range on the volume “knob” will be of practical use. At the same time, and this has been the key point for me, the cartridge needs to have enough output to properly “energize” the phono stage. To energize is the only way I can describe this and it is not simply a question of resulting total available listening volume. If the phono cartridge does not have enough output for a given phono stage the music will sound lifeless. The music won’t have enough forward motion, PRAT, groove...whatever one wants to call it; even if there is enough total available listening volume and acceptable noise levels.

So, I always look for a cartridge with output that for my typical system listening volume will keep the volume control on my preamp in a generously open (highish) range. Too low usually means that the cartridge output is too high for the overall gain structure of the system. Too high and it usually means that the cartridge output is too low and it is not energizing the phono stage properly even if there is enough listening volume; and the music suffers.