How could Schnorr signatures be aggregated across the whole transaction?
This is a feature of Schnorr digital signatures (ECSDSA) that did not exist in the digital signature scheme (ECDSA) that we are currently using. You should not compare the two multisig schemes together, the current design is a workaround.

Schnorr allows you to "aggregate" multiple signatures into only one signature by combining both private/public keys in the process of signing and produce a single signature (r,s) based on them. As a result you should only see one signature and one public key in your Schnorr transaction scriptSig and the output scripts (scriptPubkey) should also only use a single public key.

Take a look at this answer for a simplified collective signature scheme to get the general idea of how we only have one signature/pubkey, MuSig adds some additional steps to this process to prevent certain attacks.