I haven't tried rehabilitating cross head screwdriver tips but on occasion have had to grind a little off the tip of Phillips drivers, mainly of less than #1 size, when I have found that they will not seat securely in the screw head.
I'm not sure whether the problem lies with the manufacture of the screw or the driver, or possibly both, but unless the driver is sitting firmly at the top of the screw head a stripped screw head is almost inevitable.
As for slotted head screws, if you are trying to get a decent finish on the work, it now seems almost inevitable that you will have to grind a driver to fit the screws you are using. There seems to be no standardisation of any form here, the most annoying being large wood screws with very narrow slots which will destroy even a well fitted driver in no time at all.
End of today's grumble.
Pero