In theory it would be fine for a projector, but in practise it isn’t. A projector isn’t intermittent - it’s continuous-motion but the film in the gate is held steady enough for projection so the film is not quite as steady as you may think. Most other machines that you can convert into a scanner including old telecines would not have been designed with keeping the film completely steady in the gate in the first place.
If you don’t need a global shutter for your particular scanner, then sure you can buy a rolling-shutter camera. That will be the exception rather than the norm though, the norm would be you would either need to engineer your film transport to be perfectly steady or you just use a global shutter.
It’s also one more thing that can go wrong. Even a finely tuned machine that does what you need could develop an issue over time, maybe you increased the speed of the machine or made some other “upgrade” or just general wear and tear. You wouldn’t try making a DIY scanner with a line-sensor (like the Scanity) as that would take serious engineering to get it right. My point is that there’s no point in spending a fortune engineering your film transport and gate to get the film completely steady when you can just buy a camera that does what you need and will solve that problem.