Merged mining: are there any ways to prevent it? Supporting merged mining allows a cryptocurrency A to improve the security its blockchain (increase the hash rate) by accepting work done on the blockchain of cryptocurrency B through insertion of a hash of a valid A-block.

Is it possible for cryptocurrency B (say Bitcoin) to prevent its blockchain from being used to effectively enhance the security of a rival coin? (I am assuming the 'A'-hash insertion takes place in the coinbase, which is normally used for entropy).
It should be possible for the parent coin protocol to prevent being used for merged mining, by eliminating the ability to populate the coinbase transaction with random data.

Merged mining works because it is possible to inject a hash of an auxiliary block into a block of the parent blockchain.

The coinbase block does need to contain some random data because otherwise miners would hash to the same values and it would restrict the range of the hashing function.

However if the source of this entropy is restricted to a well-formed address (remember all bitcoin addresses are unique), and a consequence of putting the address in the coinbase is that it will be credited with the mining rewards, then it would not be possible to insert the auxiliary chain hash without forgoing the parent chain reward.

To my knowledge the provision of a bitcoin address + nonce within a certain range, would be a sufficient source of entropy for hashing purposes.