I'm worried about the Tomb Raider reboot because it might cease to be Tomb Raider in the gameplay sense.

You have to ask yourself: why do you play Tomb Raider?

If it's just for the character then I find that kind of disturbing. I never played Tomb Raider before Legend (the first semi-reboot game), and to me the franchise seemed to primarily focus on platforming and environmental puzzle-solving with PS1-era combat tacked-on. My favorite Tomb Raider so far was actually Anniversary because it had less of the crappy combat and more of the great puzzle-solving. Basically, I play Tomb Raider to actually RAID TOMBS.

If it were me I'd just make a game more like Underworld (the last one before Guardian of Light) but with either Uncharted-style combat, or no combat at all. In my opinion th most challenging and dangerous enemies in Tomb Raider have been the traps and pitfalls.