An Operational Amplifier is indeed a "Voltage" amplifier. It increases the amplitude/gain of the input audio signal. But on the Aiyima it also creates an "Inverted Audio Signal" from the original input. That's why there are two dual Opamps. The first stage amplifies the input signal and the second stage inverts the amplified signal for each channel. They are daisy-chained.
The TPA3255/3251 are differential amplifiers. That's why they need two identical signals out of phase 180°. So in theory you could add a balanced input signal and bypass the opamps.
Ok, so all the opamps sound the same?. Of course not. The same way not all amplifiers sound the same. The same way not all the DACs sound the same. The same way not all speakers sound the same. There are special characteristics that make each component unique.
Do you think all capacitors sound the same? Then I invite you to mod one of your speakers( change capacitors, at least the one in series with the tweeter for a better quality Film capacitor and leave the other stock. Then configure your amplifier or your player to Mono and then play with the Balance back and forth. But first leave the modded speaker running for a couple of hours before doing the comparison. You can use this test to compare different speakers as well. You can use this test to compare different opamps in the Aiyima ( because it uses one for each channel, you can try 2 different Opamp at the same time) if you use windows then you can use Foobar and a down mix to Mono addon and then play with the Balance from windows audio settings.
If you try this and they sound the same so be it. But it is very likely you will be surprised.
But no amplifier, preamplifier or Opamps will take a poor signal and make it something out of this world. Distortion accumulates during the audio chain. It is the square root of the sum of the square of each individual distortion, if expressed as %. If expressed as dB it's more complicated than that because you need to use Logarithmic operations.
If your input signal is 0.1% THD and goes into a amplifier with 0.0001% THD you total THD will be 0.10000005%, so better pay attention to your sources. But ultimately we don't listen amplifiers, we listen to speakers. And if your speakers have 0.6% THD then...