No, GME was massively, illegally overshorted.

There were 1.3 (2.9 at it one point) as many GME shorts (promises to return gamestop shares) as there were actual gamestop shares.

That's called naked shorting and it's been illegal since the 2008 financial crisis.

Of course, SEC regulations only apply to poor people, not multibillion dollar hedge funds owned by multitrillion dollar hedge funds, so they're going to get away with it, but this was a pretty unique case.

There being so many shorts compared to actual shares makes a short squeeze very easy. If GME was only, say, had 1/5th as many shorts as shares they'd need to convince a lot less GME holders to sell to cover their shorts. As is they're royally fucked because not only do they need the majority of GME holders to sell to them, they need the people they borrowed the shares they're using to short from to sell them those shares back to them afterwards.

Nah, shorting will still be a thing, they just won't be able to short a company by 130% and get away with such a craven bet.

They'll just implement some kind of capital barrier so poors can't do shorting anymore

In this case GME was very very highly shorted. Kind of like an overextension.