Processing power and frame rate is why we have crop sensors at all.
how is an aps-c sensor reducing the bandwith?
21 mp from a fullframe or 21 mp from a aps-c .... where is the difference in bandwith or needed processing power?
Smaller pixels = smaller amount of data, of course.

Which makes smaller RAW files, which take less time to process.
There was an old article I read a while back, put out by Canon explaining why we have crop sensors at all. From memory the whole reason was file size and processor performance at the time. Cheaper sensor cost and other things were not an issue initially.
Um, what?
I guess you missed my last line there.
21mp from crop = 21mp from ff
the actual data don't care of the sensor dimensions, it only cares about the number of pixels (and some other crap, but not the sensor size).
So I think you've either mis-read, or remember only parts of the explanation. E.g. for same pixel
density, FF would yield more data thus needing more processing power. But for same MP count, it's the same between crop and ff.
I don't know if yield makes the difference between ff and crop, I know in ICs the big components get much lower yield.