The data block would be modified but the signature of that block can’t be recomputed without the key used to sign it
Isn’t that also true of an encrypted checksum, though? For some plaintext block q there is a checksum r, but the attacker can only see and modify the encrypted q (Q) and encrypted r (R). How any change to Q would modify q (and R to r) can’t be known without knowing the encryption key, but the attacker would need to know that in order to keep q and r consistent.
Do you live in a utopia where you get as much beer as you want without having to pay for it, or do you live in a dystopia where you have to pay to be able to speak your mind and only in limited quantities?