The SHRA was the direct result of the anti-vigilante sentiment that had been built up over the years (in universe). Spider-man has been sued and trashed in the media. and, sure, it would be even worse in real life. he'd also be trolled. there would be people goading him into fights or spending a lot of their time trying to learn his real identity. i'm sure that there'd be impostors and faked false allegations. but i think Punisher is treated somewhat realistically in the comics. the heroes dislike him. the villains dislike him. and it's only a minority of law enforcement that gives him a pass.