There's very few games that do this, though.
Almost no vehicle-based games map mouse X:Y to vehicle theta:phi. I'm not saying I want a FPS to control exactly like No Man's Sky vehicle controls; I'm just saying that the basic idea that player input should trigger game physics should be explored, particularly in sims, to figure out a movement and aiming scheme that causes real-world tactics to emerge naturally from the game rules.
The character doesn't turn as long as the crosshair doesn't touch the invisible boundary. It's not too bad, but it's completely unnecessary.
It's also still not physics-based movement.
As an analogy, Gran Turismo 4 (now old enough to drink) gets driving physics mostly right, so the optimal racing lines on various courses are the same as in the real world without any special programming to force things. On the flip side, since there are no crash physics, the optimal way to overtake opponents is to smash into them at hairpin turns and exploit the ricochet to maintain speed. As a result, time trials feel realistic, but a core skill of real racing, how to overtake other vehicles without causing an accident, is not only something you don't really need to learn, but sub-optimal. Bumper car tactics are fine in Mario Kart, but in GT4, it feels silly. Optimal tactics emerge from the game rules, and the only real fix is making crash behavior at least slightly more realistic.
Zero-inertia, weightless weapons with pixel-accurate, unbreakable sight pictures are the FPS equivalent of bumper-car physics. By making it trivially easy to acquire and hit targets, there are massive gameplay effects. It's not a big deal in Call of Duty, but it makes games like Red Orchestra 2 feel like the GT4 of shooters. All this effort goes into simulationist aspects, and at the end of the day, the optimal way to play is not that much different than Call of Duty in hardcore mode, and real-world WWII tactics are a total waste of time. What I am saying is that if a sim is to have real tactics work, instead of people tapdance-twitch-sniping with light machine guns, then gun handling and player movement need to be physically grounded. A loaded M240 should handle like the nearly 30-lb weapon it is, not like a laser glued to your eyeball. You should move like a human, not a hummingbird.