Re: Stainless pole piece?
Yes, let's be specific. There are many alloys of steel, some called stainless. They contain a minimum of 11.5% chromium per weight (so they're sort of like chrome but not).
In theory you could make a steel that is
magnetically soft and thus solve both problems. The Ibanez SZ models have stainless pole pieces on the pickups, or at least that's what they look like. No telling if they're magnetically responsive or not.
As for stainless being magnetic, there are already electric guitar strings made of stainless (no telling what alloy though). Those have to be magnetic because that's how pickups work (see interview of Seth Lover by Seymour Duncan): the magnet in the pickup magnetizes the strings temporarily (due to their proximity), and they being temporary magnets cut across the coil in the pickup, creating a signal.
So basically, you could do what you described, you'd just have to test out alloys to get the magnetic permeability you'd want, and there's no telling if you would have to sacrifice chromium content to get it (which basically determines how long it resists corrosion: they use some high-chromium content alloys on aircraft, on which I work).
Seriously, though, it's about price point. If you're willing to pay for $5/screw or even $50/screw exotic alloys that resist corrosion very strongly
and are very magnetic, you can. I've ordered screws for aircraft that, due to their location, had to be ultra-strong, when fixing stuff. Some screws I ordered recently, in fact, were $12/each. I doubt that little difference, however, in tone, is going to warrant a major pickup manufacturer adopting them. But you could always order some for yourself

I've thought about it many times.