Accidental powershields and other similar fighting game mechanics are just a sad part of the genre. I find myself getting more powershields then say I got in Melee but I wouldn't call it a significant margin. You can't tell me you haven't laughed at an accidental power shield in Melee when it reflected a Samus charge shot and kills her. Ya that's not a reason to keep the system and if it is possible to fix that's awesome but I'd hardly consider it a problem. It's just a function of the genre.
Not quite. In Melee you had to time the powershield; any powershield that was "accidental" in Melee was only accidental in the sense that you simply wanted to protect yourself and happened to react right in the nick of time. You can get an accidental powershield in Brawl and Brawl+ without timing it because the window for powershielding in Brawl starts when the shield comes up, not when you hit the shield button.
Consider this scenario: you whiffed a smash attack. Your opponent was slow to react, so he tries to punish, but he didn't manage to hit you before your shield came up. Let's say the events unfolded as such:
Frame 1: You hit L or R while your Smash was still in progress.
Frame 11: Smash attack's IASA frame, shield came up.
Frame 12: Enemy's attack hits your shield.
If this happens in Brawl, you get a powershield - the window of opportunity started on frame 11, the frame your shield came up. If this happens in Melee, no powershield happens - the window of opportunity happened on frame 1, when you hit L or R. The window came and went before your attack ended.
Additionally, in Brawl the attack could just barely graze the outside of your shield and a powershield would happen. In Melee, the attack has to penetrate a certain distance into your shield. (Incidentally this is why reflecting slow projectiles would sometimes fail in Melee - often the projectile wouldn't end up deep enough into your shield on the frame it reached you, negating your powershield even if the timing was right.)
There's also a 3rd problem with Brawl+ powershields that as far as I know hasn't been fixed: powershields aren't being affected by the shield stun code. Powershields are supposed to have the same shield stun was normal shielding. However, if for a given attack the vBrawl shield stun is 4 frames, and in Brawl+ it's 12 frames, a powershield will only get 4 frames of stun when it's supposed to have 12, giving you a huge frame advantage that's not supposed to be there.
If you're good enough at shield-tilting you should never be getting shield-stabbed anyway.
I'm not advocating that we weaken shieldstabbing, but this isn't entirely true. During shield stun, the shield will revert to its neutral position no matter what you do. So if you get hit by a multi-hit attack, you can't tilt your shield for any hit after the first.
Then there's the fact that you can't quickly tilt without getting an accidental dodge unless you have an insane amount of control to tilt the stick in 1-2 frames without overshooting the halfway mark. (Only exception is tilting up if you have Tap Jump Off, since you can smash that without adverse effects.)
The best solution is still to not waste your shield (i.e. not leave it up when not being attacked) and don't let it take that much damage.