one reason: price.
From TI website (1K unit price):
TPA6120: $1.56
OPA1622: $2.9
BUF634: $5.68
I read somewhere TPA6120 is actually re-branded ADSL modem transformer driver, that is why we see such crazy slew rate at 1300v/us. If read the data sheet really carefully, I have a feeling that even data sheet writer think it is a bad choice for audio: it is a current-feedback opamp which is very hard to avoid oscillation.
I don't think BUF634 is good choice either. You need add another opamp for voltage amplifying and insert the BUF634 into the feedback loop.
OPA1622 might be the only opamp designed from ground-up for headphone amplifier, It get really good spec in noise, idle current, slew rate, short-circuit protection etc. (another one might be NJM4556 as used in O2, but the idle current bit high at 9mA, no short-circuit protection). It is just hard to DIY for the VSON-10 package and do proper layout. I really hope Topping can come up a design with OPA1622, it is not too expensive.