Power of two FT's were not all that slow in the 1980's. All the main players had some variant of the 2,4 split radix algorithm by then although it wasn't published until I think 1984 (although ISTR we now know someone had published it in 1968 but no-one had noticed). Jodrell Bank could do lengths of the form 2^n.3^p.5^q.r (where r was a prime) by then. We could do 1024x1024 images at a push (512^2 was routine) and the VLA could do 2048^2 with some discomfort for other users.
What made big 2D FFTs slow back then was paging and transposing the data so that your FFT was always running over closely spaced local data. Way more effort went into the block transpose with the absolute mininum number of page faults than went into optimising the core FFT (although it did even back then have go faster stripes for certain cases).
There was soem playing around with Winograd FFTs for radix 6 and 10 but they never gained populairty on our site.
Paradoxically on modern CPU's pure power of two FFT's fight with the hardware cache algorithms and other non 2^N radix choices can be faster.
For looking at a few spot frequencies the DFT could sometimes win out.