Indeed, but in the two balanced stages of gain there will be 4 active devices. A single ended 2 stage design will only have 2 active devices, so half the number of active devices of the balanced stage. Plus there will be the extra components required for the 4 active devices over the 2. Then you have to make sure the active devices in each stage are absolutely identical, which is not a requirement for the single-ended design. I still maintain that there will be more parts involved in a balanced design then in a single-ended design including the ones in the signal path.The phono cartridge is a balanced source.
So if you have a balanced input the cable can have less influence on the sound- perhaps none at all.
If the internal circuitry is fully differential and balanced, you have more immunity to the power supply. You also have in theory 6dB less noise per stage of gain.
The statement highlighted above is false and is a common myth about balanced operation. We have only two stages of gain in our fully differential balanced phono section, which is zero feedback with passive EQ (executed in the differential domain, so no issues with tube drift and the same number of parts as you see in a single-ended passive EQ circuit) and it works fine with LOMC cartridges straight in. There is not 'double the parts' nor 'double the number of active stages' because to execute a differential amplifier you do not need twice as many parts as the same gain stage executed single-ended.
What you get instead is a simpler signal path; most phono sections that can work with LOMC cartridges require three stages of gain or two stages with an SUT; either way more frequency poles (especially if an SUT is used) than in a fully differential circuit.