As many already said, TR in its core is grid based exploration puzzle-platformer, like original Prince of Persia, so original controls make sense, and there was big backlash in TR community when CD changed them with Legend (personally I'm fine with both, since the core gameplay was preserved, unlike Reboot which has nothing to do with actual TR, except for the name).
There is a reason why, once upon a time, before YT, when Game Trailers was THE place to go to for gaming video media, they made all the new interns play original Tomb Raider (among other games).