It is critical to keep "block" message relaying (propagation) times as low as possible, to avoid creating incentives for miners to skip transactions. Thus, a signature cache ensures that "block" messages are largely already verified, by the time they are received.
If miners are already shrinking their blocks due to propagation time, maybe it's time to consider that protocol improvement suggestion in the scalability page, about not sending the entire block every time, just the portion your peer doesn't have.
I don't know what exactly could be send instead of the body, though. Even if my peer has all transactions in his cache, doesn't he need to know the exact order I put them in my block in order to rebuild the Merkle tree? So just sending the header is not enough. Is there a shorter way to identify a transaction than its hash? Perhaps just an ordinal of the hash... you assume your peer has the same transaction pool you had, then as the body of your block you send a series of numbers which represent the index a tx hash would have in a sorted array with all of them? Not sure that would work frequently... plus, the hash is probably small enough, it shouldn't be a big deal to send all of them.