To add to this, it seems that there's a split of opinion between the Punisher's original creator and the one who ended up writing his first comic run. When the Punisher was created by Gerry Conway as a second rate villain for Spider Man, he was essentially a tacticool version of Kraven the Hunter, but instead of wanting to hunt Spider Man for sport he wanted to kill him because he believed in killing criminals, a direct antithesis to Spider Man who has often been portrayed not just catching criminals, but following up with and trying to rehabilitate them.

Gerry Conway wanted readers to see that the Punisher was a broken and sad man who was lashing out at those around him, but of course comic fans thought he was a super badass guy with guns. Since he became popular, he eventually got his own series - but Conway was still working on Spider Man, so after a mini series written by Steven Grant the ongoing series was started with Mike Baron as the writer.

Baron is the one responsible for permanently cementing the character in the Marvel canon as being a good guy instead of a bad guy who occasionally teams up with the main characters (and the one responsible for the comic abomination in the OP). It's worth noting that this happened in 1985, while the War on Drugs was at its fever pitch (take a look at this handy graph!), and so the idea of a reactionary superhero really embodied what a certain cohort of comic readers wanted to see - a cop who wasn't held back by red tape or ethics.