The players don't have to map in my games. That's a player role that isn't really relevant in more modern editions of D&D. I don't know of any reference to players drawing maps in the D&D 5e rules, for example. Even back in the day when it was an assumed part of the game, the person who got stuck with mapping was the person who was in the bathroom when roles were assigned. Nobody liked it then and I don't imagine they'd like it now. Only now it's made more irrelevant through the use of Roll20 at our table - the map is on the screen, revealed as they move about.
Now, characters often map in my games, when it's useful to do so. In certain scenarios, particularly those involving overland journeys, mapping is a useful Activity While Traveling which helps create an asset that allows the party to avoid getting lost on the return trip. Other times, I offer gold for source maps as a further incentive for players to have their characters draw maps instead of, say, keeping alert for danger.