In my experience some games are ridiculously finicky about this - won't allow remaps of this sort of thing, etc. It's an enormous pet peeve of mine, since, if Duke Nukem 3D from the 90s could remap controls any way the user desires, why can't more modern games? This is absolutely inexcusable in ANY game.
My assumption is that in some cases, it's laziness/sloppiness when porting from a console. In others, maybe an idiotic "oh, nobody would ever remap this, everyone plays THIS particular way"
In my FPS type games, I hate WASD as it's used, I'm typically:
Left-Mouse - move back
Right-Mouse - move forward
W - Jump
S - Crouch
A - Strafe left
D - Strafe right
L-SHIFT - fire
L-CTRL - alt-fire
SPACE - use/open/etc
The vast majority of games allow remapping, BUT, some stubbornly do not, or only allow some controls, but not all, to be remapped.
I've used GlovePie for Dead Space. I've noticed that both The Forest, as well as Brütal Legend, simply do not let you remap movement to the mouse. Even using something like GlovePie, the game somehow ignores/bypasses it at least partially, making for a miserable experience.
NOTE: at some point during my use of Windows 7 (after some update or other, I think), GlovePie would crash if I tried to map things via the GUI. This would happen even if I went to the latest and greatest, or a step or three back in versions. I haven't tried it since I upgraded to Windows 10, though. However, if, instead, you use a config-file and load that in, it works fine, at least for Dead Space.
EDIT: sorry, this turned into a semi-rant... it's frustrating, to say the least.