I have a bit, I use right now, on a Milwaukee impact screwdriver that sticks inside screws badly. It has seen a lot of wear and tear and when it sticks there is no "wiggling it back and forth". The damn screws won't come off with a hammer! I have to screw the screw back into the hole of a piece of wood and use the leverage of the drill to "snap" them apart.
This is from using the non-Robertson (SquareDrive) screws on the Robertson bit. Impact drivers make this situation worse, faster. The square edged sockets of the screws cut into the taper of the Robertson bit and eventually put notches in the corners of the bit so the screw can wedge itself onto the bit by hooking onto the edges of the notches..
Yeah, even the good Robertson bits need to be replaced every few thousand screws. Funny how the old cheap ones are still working but the new ones, no matter what you pay work for a few weeks.
Don't buy the Robertson coloured bits at HD, in Canada. I have tried a few that came out in the last year, or so, and they are good for a dozen screws and then garbage. Yes, they appeared to have hardened insert tips in them, too and they were about $4 each.
Now having said that I have been using square drive screws for probably
25+ years exclusively except when they are not available. I have no intention of switching.