What if block N were based not on N-1 but on both N-2 and N-3?
Objections that come to mind initially, I'm sure there are more:

You don't want to split the hashing power into two halves because that would make it easier for an adversary to get 51% of that halve: 25% of the total or even less if the halves are not exactly 50-50.
The idea behind Proof of Work is to concentrate as much work as possible behind one and the same chain and make that the level-to-beat by an attacker.

If you force odd transactions into odd blocks (and vice versa) then you still have 10 minutes block times for all transactions.