I am referring to the approach taken in this video, at about 00:43. I know that the op-amp "tries" to balance the voltages at its both terminals but is it a completely correct approach to take V+ = V- when deriving the op-amp's closed-loop gain? As far as I know, in practice, V+ is never equal to V-. But from a theoretical point of view, would it always be correct to assume V+ = V- when calculating the op-amp's closed-loop gain?
Yes. V+ = V- in cases whenever an OP-AMP gives out stable output and negative feedback dominated cases. In the real world, they are not equal. But almost equal. The difference between V+ and V- is almost zero and the gain of the OP-AMP is huge. But for a theoretical purpose, we just take it as zero and assume the gain of the OP-AMP is infinity.
If you want a better answer, use the formula V0 = A.(V+ - V-). In the video, V+ = Vin and V- = R1.V0/(R1 + RF) and then derive V0.