I had an idea for a payment scheme that uses key derivation, but instead of the payee deriving the addresses, the payer would do it.

It would work like that:

The payee publishes his master public key
The payer generates a random "receipt number" (say, 25 random bytes)
The payer derives an address from the master public key using the receipt number and pays to it
The payer sends the receipt to the payee
The payee derives a private key with that receipt and adds it to his wallet

Advantages:

It increases privacy by avoiding address reuse
The process is asynchronous. The payee is completely passive in the payment process and isn't required to provide new addresses before each payment (so no payment server required)
Its usable as a replacement for cases where re-used addresses are the most viable solution (like putting an address in a forum signature or as a development fund in a github readme)
The receipt also acts as a proof of payment that the payer can provide to the payee
Also, if the master is known to belong to someone, this also allows the payer prove to a third-party that the payment was made to that someone. If the output was spent, it also proves that he was aware of the payment and has the receipt.
Its a really thin abstraction layer that doesn't require much changes

Disadvantages:

Losing the receipt numbers means losing access to your funds, they are random and there's no way to restore them
It requires sending the receipt to the payee somehow. Email could work for that, but a better defined channel that also can talk to the Bitcoin client and add the receipt would be much better.

What do you think?