All of what you said is true.

Yes: compensation is needed to account for non rectangular sampling (see the Polar reformat or the Stolt interpolator). Yes: non-straight and level flight paths result in degraded or even useless imagery unless the deviation is small or the FFT-based algorithm is specifically tweaked for it. Yes: various algorithms make assumptions that may be violated (e.g., planar wavefronts).

But again, I think it’s just the computational efficiency of the FFT-based algorithms for real-time use.

As a random thought, a lot of radar engineers that don’t start with SAR are perfectly comfortable reasoning about Doppler. Particularly with regard to detection of moving targets. Maybe that’s a factor, too.