There is that spell from XGtE, Sickening Radiance that can really put a hurt on a party as well.
PC suffer more from exhaustion as they survive encounters -- exhaustion only matters to those that hold the field as those that don't are dead. However, if a party that is more into scouting and information gathering could setup encounters so that the NPCs start with levels of exhaustion.
In OotA, exhaustion works fairly well to setup the idea of a long distance chase/pursuit. It constantly puts a time pressure on the the party, rest and risk getting captured again or keep moving but become exhausted. So if the DM is really hitting this theme, I can see it working. But then it becomes a pacing issue where at some point, the DM has to provide a safe (if temporary) location or let the party use their wits to create one.