Block Ciphers / Kerckhoffs Principle
In other words, how hard is it to decrypt a given ciphertext without knowing the details of BLOCK.


Pretty easy; all you'd need to do is ask for:

ENC(0x000..0001)
ENC(0x000..0002)
ENC(0x000..0004)
ENC(0x000..0008)
ENC(0x000..0010)
...
ENC(0x400..0000)
ENC(0x800..0000)


For an $n$-bit block cipher, that's $n$ queries.

Then, you find the linear combination of the above values that gives you the known value ENC(BLOCK) (for example, by Gaussian Elimination); by the homomorphic property you listed, that immediately gives you the value of BLOCK

This same strategy can be devised as a known ciphertext attack, using $n+\epsilon$ random known plaintexts, that'll allow you to decrypt any ciphertext with high probability.