I like your approach, but how this approach will differ if you assume that the op amp in saturation (No feedback)Feedback be dammed, here is why the inputs of an op amp are assumed to be "equal or very close" in many cases.

Take a traditional op amp with a +/- 15 volt power supply. We will look at it when the output is NOT in saturation, or the output is in the range of

-15V <= Vout <= +15V

The output of an op amp is given by the equation:

Vout = Av * (V+ - V-)

where Vout is the output voltage, V+ the + input, V- the - input, and Av is the open loop gain.

Now even with an old fashioned 741 type the open loop gain is 50,000. So let us see what is going on at the input for the largest signal the amp can make:

Vout = +15V = 50,000 * (V+ - V-)

(V+ - V-) = 15V / 50,000 = 0.3 mV

So the largest signal the amp can make is produced by a voltage difference of only 0.0003 volts.

Hey, that's damn close to zero so let's just assume it really is zero and get some work done.