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
The so called ''moving parts'' by an (MC) are cantilever/stylus
and coils. Those are fastened to the joint pipe in which also
''tension wire'' is fastened in order to connect moving parts
with the generator. It is obvious(?) that cantilever /stylus
combo weights ''nothing''. So the most weigth is in the
coils. The number of windings determine the output. So
the lower the output the lower number of windings and
the lighter the moving parts. Any attempt to reduce the
weight of the moving part means reduction of the wire jn
 the coils. One can increase the output by ''iron core''
in the coil former but this has other drawback. The ''coreless''
coils are the best but with the owest output. For those
one will need very good phono-pre or SUT.
The most noticeable noise I get when replaying vinyl is from the record surface, the phonostage noise doesn’t seem to intrude. I looked up the specs for my phonostage and it claims a SNR of 82dB for a 0.5mV output and a gain of 64dB. I’m actually using an SPU Royal N with a 0.2mV output. (I have a VPI 16.5 and a Degritter to clean the records which helps).

If you’re after a medium output the EMT cartridges with around 1 mV seem to have a good reputation for not losing the music in the hifi.
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.