you should really look into lost media, stuff gets lost on the internet all the time. and that's just the stuff people are actually caring to look for
A file on the internet obviously could be backed up by anyone, so deleting things from the internet does not verifiably restore your privacy.
A file on the internet might not be publicly accessible in the future. But that doesn’t mean it hasn’t been backed up privately.
It is the worst of both worlds.
Probably it won't, though, for most people.
Posts made after the API access was removed would not be in Pushshift.
Posts made before, are still in Pushshift. Deleting a post from the site doesn’t remove it from Pushshift.
So… kinda not anymore? At least not publicly, using the officially supported API.