Absolutely it can but that's not how Tomb Raider and Uncharted work. Mario style platforming would look weird with a realistic human, I think.
Tomb Raider isn't about platforming so much as climbing.
Well, at the time it was new so it felt like it needed some skill even if it was way slower paced than cute platformers. I guess a lot like Prince of Persia or Oddworld style platformers were also slower paced than Mario. Cinematic platformers I think they called those, Flashback, Heart of Darkness, Another World...
But yeah like when you had to do tricky for the time things like grab on a ledge, pull up, jump forward or sideways, slide down a thing, jump at the right time, hang on, etc in sequence like that or whatever, maybe while timing the whole thing to bypass traps or target moving environmental elements. And at times you could optimize your movements and use backwards jumps/rolls instead of turning around slowly and running and climbing somewhere etc to make the whole process speedier and smoother, sometimes doing that could even be required because of timed triggers or whatever, although I don't think it ever got too strict.
Anyway, they could update it to allow for more skill too, rather than less. I really enjoyed the whole moveset except when they added clunky and slow even for the time things like needing to equip and throw flares, or the dumb looking ladder climbing and crouched moving in later entries with Lara awkwardly on all fours... I guess they could also take inspiration from the Sands of Time style Prince of Persia games, sans the supernatural abilities. Those felt like the platforming needed skill also, combining that with Lara's earlier moveset style (and precision as a must, Sands of Time was great but it could feel a little loose!) could maybe work out.