Reacher never punches anyone.

Punching is bad for the hands

Punching someone -- in the head at least -- is dangerous in a fight. It's too easy to break your hand. Boxers can do it because their hands are heavily wrapped in tape, and then covered by thickly padded gloves. Boxers didn't punch at the head nearly as much, or nearly as hard back in the old bare knuckle days -- and there was throwing and grappling under the old London Prize Ring rules. The modern rules, which are descended from the Marquess of Queensberry rules, were adopted to get jurisdictions simply to permit boxing matches to happen. Under the old rules, they were often held illegally because local governments wouldn't sanction them.

The problem with the old rules were that A) with no limit on rounds (the fights went to a knockout, or one fighter threw in the towel), and B) no gloves (it's easier to get cut by bare knuckles), fighters would look like raw hamburger after a long, hard fight. It struck people as too brutal and barbaric. The Queensberry rules were meant to tame it down a bit and make it more acceptable -- which they did. Ironically, it had the opposite effect, from the safety standpoint, even if it didn't look as bad. You see, with the gloves and tape, boxers could now target the head and hit with full force. Fighters get their bell rung a lot harder, and a lot more often than the old bareknuckle boxers did. The bareknuckle fighters might have had more visible scars, but they didn't end their careers with the kind of cumulative brain trauma modern boxers often have to deal with.