I think "balancing" is an analogue concept which is an effort to reduce the effect of external noise entering an analogue audio chain.
The basic idea is splitting an analogue signal into two signals and inverting one signal with respect to the other before transmission. If noise happens on the transmission line (interconnect) then both the signals are modified by the noise in the same way.
At the receiving end the inverted signal is inverted again and then added to the other non-inverted signal.
In this way the noise is combined with an inverted version of itself and so the two noise waveforms tend to cancel each other out. The two signals are now back in the same phase and reinforce each other. They do not cancel out.
In a fully balanced system you need not only separate processing for left and right as usual, but also for inverted and non-inverted in each case.
Now you have four independent chains in the system between the source, where the splitting first occurs to the power amp outputs where the inverted and non-inverted signals obviously have to be recombined.
Remember that this is a purely analogue system so far.
If there is a digital link in the chain, such as a DAC, then it would have to have four channels with four independent DAC processors.
If such a device is hit by noise then it is by no means obvious to me that the effect on the four signals will result in the simple effect on which the idea of analogue balancing rests.
Therefore the balanced input of the DAVE must recombine the signals before processing, and the balanced output of the DAVE must split them again. The inverting op amps are simply the way this is done.
The only benefit of balancing here is that the input cable is balanced. Even though it carries a digital signal, for the purposes of balancing it can be successfully treated as an analogue signal. I do not think the DAVE itself can be sensibly balanced.
If this is a load of
then by all means have at it. Just try to be polite!