I disagree with a core part of this - no ttrpg I'm aware of let's players do anything. There's a theoretically infinite number of options, but only in the sense that's there's an infinite number of numbers between zero and one. In actual practice, there's a large but finite number of options at any given time.
The difference is that ttrpg's allow "make something up" as an available option, if you ca get the gm to agree to it. Board games (and video games) only allow the previously defined list of options. But since "make something up" is usually understood to mean things that fit within the parameters of the existing choices, the theoretically infinite number of new options aren't really letting you do anything the existing options didn't allow.
Ergo, most elements of board games could be used in ttrpgs. Whether they're the right choice for the game you're trying to make is a series of potentially very long discussions. But since this is a DnD thread, I will say there's a lot of useful tricks from games like Gloomhaven or Clank! that could be used to make the DnD experience 'better', or at least different in positive ways.
IE in Clank! there's basically a counter that goes up every time you make noise; once you make too much noise the dragon wakes up and tries to eat everyone still in the dungeon. Having a threat-clock like this (and visible to the players) can add a lot of tension and an important new strategic consideration to your dungeon crawls.