Calling the villains in Max normal is somewhat relative. A number of the villains in the Max run had trademark Ennis over the top cartoonish black comedic depictions. The Russian turned into a cyborg with boobs and Finn Cooley was another disfigured villain. Even the much loved Barracuda was a cheerful optimistic murder for hire cannibal.
I really like Ennis Max run like everyone else does but Ennis treated the Punisher as just an effective story device a single-minded SOB to be thrown into absurd situations and against despicable villains in order to get laughs or primeval satisfaction. That works fine for a comic run but for the Netflix show that isn't going to be the direction they going given what we have already seen from the character.
Mike Baron's Punisher villains on the whole were possibly more grounded and realistic than Ennis villains and Baron was on high on cocaine when he was writing the Punisher
Baron had the Punisher go after people smugglers on the Mexican border. The first ten issues of Baron's run had the Punisher go after corrupt South Vietnamese generals, ghetto drug dealers, a Bolivian cartel, Missouri white supremacists, a cult led by a proto-Charles Manson, Arab terrorists, and Wall Street inside traders.
I would not say Punisher failing to kill Jigsaw makes him look incompetent. Billy Russo was supposed to be one of the best mob hitmen in the criminal underworld. Despite some depictions of him as a Punisher obsessed gangster thug, Jigsaw is a sharp strategist and tactician which makes sense as you need those skills to kill people and not get caught or killed yourself. Jigsaw is the Punisher's arch enemy because they are supposed to have a near matching skill set. Jigsaw even got brainwashed into taking the Punishers place in the comics.
Saracen, an Arab mercenary also survived a numerous run ins with the Punisher before Frank finally killed him. I don't think there is anything wrong with highly skilled criminals surviving encounters with the Punisher a few times before they finally get killed by him. It wouldn't be very entertaining if the Punisher easily killed every villain he encounters within one or two stories.
I agree the Punisher doesn't need a arch enemy but some comic writers and fans love their genre tropes.
They are using 616 and Max villains in the show. Kingpin, Jigsaw, Ray Schoonover (The Blacksmith), Finn Cooley, William Rawlins and Curtis Hoyle are comic villains we know they are using or have used so far. These guys are relatively grounded.