Keep in mind that the complaint Uber had was with writes in Postgres affecting secondary indices that
didn't cover a particular column. As far as I know, in
all databases, if a covered column is modified the secondary index must be, too. So that does not really resolve Uber's problem.
Additionally, I can't quite recall whether this is the case in MS SQL (since it uses pessimistic locking by default, not snapshot isolation, which has different performance characteristics), but in most MVCC architectures there's the additional problem that the underlying row value could have been changed concurrently with your query (e.g., deleted or modified). While this might not seem so bad for simple row-level lookups, this gets much more problematic if you are doing something like a range query, where the index might contain rows that weren't in the database at the beginning of your snapshot. There are a variety of ways of dealing with that problem, but most of them involve increased write traffic (index sizes get even more bloated because now they need versioning information), increased read traffic (index reads that touch out-of-date rows may have to follow an undo pointer, requiring the extra seeks you were trying to avoid in the first place), more locking (for instance, you could lock the entire index when a transaction modified it to keep it consistent--but that would decrease concurrency--or you could try to do range locking--which can lead to increased probability of deadlocks and also decreases concurrency and increases contention on the lock manager), opportunistic optimizations that only work on mostly-immutable data (Postgres and HyPer's solutions is to maintain a much smaller visibility map with bits indicating whether it's safe to assume the index is unchanged), or giving up multi-key read consistency (I'm assuming if this were an option you would be using another storage engine, because lots of them can perform unbelievably well if that restriction is relaxed!).
My point being, there's no such thing as a free lunch. Personally, I'm usually extremely happy to give up on pessimistic locking for the concurrency benefits of MVCC, and index utility decreases sharply as it gets larger, but as with many other things it entirely depends on your workload. Two-phase locking actually works far better than MVCC of any sort under heavy contention with short transactions (what Uber is apparently doing), so they really probably should have investigated SQL Server or another database optimized for pessimistic concurrency control.