I agree with FreeTrade, why use a memory intensive algorithm for BirthdayHash if you're gonna fill up your ram with hashes anyway?
But either way, here is why it is worse than scrypt:
Your proposed algorithm (momentum) scales super-linearly with the number of computers that can be dedicated to solving the proof-of-work. Set up N computers storing generated hashes in a distributed hash table between them. They now have N times the memory capacity of a single computer and will fill up their memory just as fast. This could scale to pretty large N's, you don't need low latency, you could accumulate hashes on each computer and send them in batches.
And this is bad of course (would lead to centralization).
Suggested modification:
Embrace this and encourage every single miner to be part of the same DHT (Not that simple, but you get the picture), share reward between the computer generating the hash and the one that had it stored. Could work on the current P2P system already in place.
I agree that if there were a way to efficiently merge the memory of all computers on the internet this would be great. Unfortunately, the memory bandwidth would be limited by the internet and thus not pratical at all. However, I suspect that every office environment could achieve this at a slightly smaller scale.
What is the cost per unit of computational power / memory as the amount of memory / power approaches infinity? I suspect that it goes non-linear for larger and larger sizes and thus the limits on Super Computers today. Eventually speed-of-light becomes your problem.