If you do a search on quadratic or parabola with focus you will see this topic has come up a number of times.
There were big changes to the autofocus last year that helped with sct autofocus - and here is one thread with one of my parabolas:
My curves aren’t always that nice - but they are close - and I can see focus shift slowly during the night consistent with temperature change.
A key point in all this is that what matters isn’t the lateral offset of the focus error - but what impact it has on the fwhm. That’s why I say that as long as the focus position is found near the flat region of the bowl, it is good enough - particularly if a small amount of temperature drift in time would be greater than that error.
But it’s somewhat moot if the error is small in the first place.
Yes - it could reject bad ones and so forth and again I think such fits would be good given infinite development resources. But I have more pressing issues in terms of functionality and usability that I would give much higher priority.
Frank