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.
Thank you for interjecting.