Well no, because CoinJoin transactions are actually quite large, and it is necessary to settle many transactions at once using a small amount of bytes if we want to see scalability improve at all.

MuSig is just the aggregation of all signatures in a multisig. My solution for scalability leverages MuSig for transactions where you have a bunch of inputs from different people, went to a single MuSig output held by all of them. A sort of "side-chain" can be started at this point, though it is ephemeral and for bitcoin transactions only, and only exists as long as the MuSig UTXO is not spent - this would be like the regular blockchain but with a very low difficulty hat only accepts Proof-of-Works that have a MuSig signature from one of the participants (hence N will be very large).

To settle the transactions, the MuSig will be spent by the users (ideally all of them, but this is a diamond's rough edge I have not polished yet) and the outputs will go to addresses according to the predefined arrangement.

I'm anticipating that in the distant future, the vast majority of Bitcoin transactions (remember, transactions - you still own your keys) will be settled on this new layer that has nothing to do with Lightning - this is going to be the Layer that makes payment networks like VISA obsolete.