You realize that Tomb Raider needed a reboot in the first place because the old formula wasn't working. If it's not dead yet, one sure way to kill the franchise would be to try to make it a pure 3D puzzle platformer. If anything, RotTR bombing means that it needs to go even further in widening its audience.
Personally speaking, I bought, played, and enjoyed the reboot, but was/am put off by the emphasis RotTR placed on going back to the old formula. I have no idea what the gameplay is really like, which is due to the muddled marketing the game had. Between that and the XB1 exclusivity, SE has turn me from someone who had Tomb Raider on my 'To Buy' list to someone not caring about their game at all.
The problem is that the original formula is so inherently a product of it's time. It's right at the very start of the 3D era with controls that proved to be great for one or two iterations but quickly got surpassed by better control schemes. Seemingly no-one can marry the original idea and ambition with a modern control scheme without watering it down to yet another action game or flat out remaking the original game. The puzzles in the original are largely built around the restrictive controls in a similar way to the original Prince of Persia.
The 2006 (IIRC) was alright but by the the end of that trilogy things had strayed towards action fairly heavily. The remake of the original they did with that engine was fairly decent though.
If CD want to make an action game they should use the Legacy of Kain IP and just leave TR alone untill someone can figure out how to integrate a tight control scheme with environmental puzzles. Hell, maybe first person is the way to go along the lines of Portal.