As an example, consider your (and Mike's) proposal to propagate headers and/or transaction hash information, rather than full transactions. Can you think of a way to attack such a system? Can you think of a way that such a system could make network forking events more likely? I'll give you a hint for the latter: reorganizations.
Are you talking about the case where I mine a block with one of my own transactions which I haven't announced, so you have to make another request for the missing transactions before you can verify it? If I refuse to provide the missing transactions, then no-one will accept my block and I lose. If I delay announcing the missing transactions, competing blocks may be found in the mean time, so this is no different to delaying the announcement of the block itself which has no benefit for me. What am I missing?