Why wouldn't it be recommended to use the old screw and 'rehab' it to make it usable?

It's done all the time in the trade.

It's certainly more of a 'true restoration' than buying a new mfg'r one from an internet company and making it work. That's if restoring something as small as a screw matters.
I think it does. Simply replacing parts is just that. Sometimes it must be done. But too much of that is done today and still called 'restoration.

If you happen to have an original lying around and is in great condition, then it may be usable. It likely won't 'clock' into position correctly but there's always that chance it will.
It may take some fitting to make it look correct and fit level with the existing plate.

Lots of restoration work involves replacing and/or repairing just screws. You can nearly make a living doing that on high grade firearms. Some need a handful and more repaired on one firearm.
That includes fitting for proper alignment if needed on the gun, any engraving necessary and the final finish. The latter may not be a pristine finish either.
A subdued, worn or even lightly pitted look may be needed to make it look right on a specific gun (much like this one).

I've done probably hundreds of these over the yrs and never had to send one out for someone else's help in finishing it up.

If you don't have an orig to perfectly replace it and have it look correct, then the other ways are to rebuild the orig or make a new one and make it fit and look correct.

If 'it would not be sensible' means that it takes too much time,, I can rehab a screw like this in much less time than I can turn one out on the lathe.
You will never know it's a 'recap' either.

If this is "not out of principle", but for various concurrent good reasons" I'd like to hear what those good reasons are that 'professional restorers' would tell me.