Prophecy2k
Veteran
I don't know if it wouldn't exist, but it might exist with a smaller budget. I'm sure SE could fund many Tomb Raider games, but they're probably only willing to fund as much money as they can turn a profit on. Whether they have a billion dollars lying around is kind of irrelevant.
If SE didn't think the funding and other terms would be beneficial, why would they make the deal? They can't be so stupid to cut off all those PS4 sales for no reason at all.
It might exist with a smaller marketing budget without MS' involvement. In terms of development I don't see MS having any influence over that at all. The game will be developed over a standard dev cycle, maybe will be in full production for 18 months. I don't imagine that MS' deal money was used to enlarge the scope of the game, but of course we'll see when the game releases.
Naturally however, these deals are about one thing... risk.
For SE signing a deal like this, it's down to them feeling sufficiently anxious about the marketability of their title and the kind of returns on investment they will see. By sharing that risk with MS, by signing a deal for them to put in some marketing dollars, they effectively mitigate that risk to a great extent.
The downside however is that they now have a smaller addressable market to which they are able to sell the title, so there's next to no reason for them to put any additional money into the development of this game, since it would invalidate the point of the deal. Equally for MS, it would make little business sense to pump significant additional money into the game's development, since more money =/= a better game, and the whole point of a deal like this from their perspective is that they leverage the power of an existing and popular franchise brand in an attempt to sell more Xboxes. So the only reasonable place to put any additional spend from MS's perspective is in marketing, since the addressable market for the game is smaller, and thus it makes sense for them to have to spend more to maximise game sales on Xbox platforms.
So given the above, I can't see any solid business justification for believing the game's development budget, scope or design will be impacted positively by this exclusivity deal. In fact there's more of a likelihood (however remote) that the opposite could occur.