Gains of both amplifiers have to be exactly the same, otherwise common mode noise will get converted to normal mode signal. It requires some form of cross-feedback to keep gains exactly the same. Phono preamp in addition has RIAA equalization that changes frequency response within audio band by 40dB (100 times). I suspect, that it would be very difficult to match it in both "legs" of true balanced phono stage.This statement isn't quite correct. To prevent issues with RIAA equalization, you simply do the EQ network in differential mode. This eliminates issues with matching and gain differences.
A bit of audio history since this is relevant: we built the first fully differential phono sections for home use in our MP-1 preamp, introduced in 1989. As such is was also the first balanced line preamp, tube *or* solid state (again, for home use). At the time the XLR connector was the only game in town so that's what we used for the phono input. We had no idea at the time that a product like this should do anything other than support the balanced line standards (AES48) so that is what it did and does.
The correct phono connection is: + and - outputs of the cartridge are pins 2 and 3 of the XLR. The tone arm and turntable ground is the shield of the interconnect cable and ties to pin 1 of the XLR of each channel, so no ground wire is needed. You'd be surprised how many cable manufacturers there are that think the ground wire is still needed :)
This connection is so quiet that we've used unshielded twisted pair with a ground wire (what we've come to call a 'twisted triplet'; but we've also used Kimber braided wire) and its noise-free. But one thing that has been pointed out here that is really important is the CMRR of the input stage. Of course transformers do this really well, but since we're sort of known for transformerless operation, the other way to do it is with an input gain stage that has as high CMRR as possible, combined with the lowest noise.
Obviously opamps work great for this but we wanted to use tubes, so the input circuit is a differential cascode which employs a 2-state CCS (single-stage CCS circuits leave performance on the table). If you want low noise and high CMRR, this type of input circuit (which is common in a lot of solid state circuits as well) is really the only way to go. Because tubes drift and because matching components is tricky, we sorted out the differential mode EQ and as far as I know we're the first to do that by decades prior to anyone else. Differential mode EQ insures that both outputs of the phono section (inverted and non-inverted) will have the same EQ regardless of how much gain imbalance there might be. To prevent common mode noise from becoming differential mode the simple bit is making sure that any ground in the gain circuit is common to both phases- common sense :) In this regard layout plays a role as well, as the designer will find that certain parts in the circuit are best placed as close to each other as possible to maintain noise immunity.
The main downside we encountered was the reluctance on the part of dealers to deal with the balanced input since it meant changing out the tone arm cable; some thought the arm had to be rewired which of course it doesn't :) The advantage of operating balanced at this point in the signal chain is that as long as the tone arm cable is low capacitance, the cost of the cable isn't important- how its wired is. So you can have a $200 cable sound just like a $2000 cable. Cable immunity was a big incentive for why we developed a balanced preamp.