Other than being in the military, I have never had to regularly navigate via map and compass in the field in any precise way, I take estimated traveling azimuths and adjust as I go along. But I always take a topo map with me and refer to it as I go along my track, it helps me keep oriented as I'm traveling so that my chance of getting lost is far less. I also use a GPS regularly. Between the two I've never had a problem with knowing where I was or where I needed to go.
That being said, if I am in really dense forest then yes, I'd do a more precise job of navigating and I'd check my map and compass far more often but when that happens I've never needed the precision of having a perfectly oriented map. I would usually lay the map on the ground and the compass on top of it, adjust for the grid to magnetic north declination by turning the compass away from the grid north lines slightly, identify an imaginary line to my target, move the compass close to that imaginary line and estimate my traveling azimuth. That's good enough for general navigation but it wont be very accurate if you are trying to find your way back to your truck or a downed elk. On the other hand, since I've always got a GPS (with extra batteries and a back GPS too), I just mark a way point and navigate to the spot.