That's a nice idea but I still don't see how it reduces the number of onchain transactions required. If anything it increases the number of transactions required because it performs transactions on every block.
Well first of all, settlement nodes won't be spitting out multiple L1 transactions in each block. It will be just one transaction, and all of the output addresses are added to that one transaction.
MuSig will drastically reduce the size of this one transaction. Instead of several inputs and outputs, it will have several outputs but just 1 input.
MuSig addresses are multisig addresses where the public keys are combined into one shared public key, instead of using all those individual public keys individually. The same goes for signatures - everyone still has to make a signature, but now they can combine it into one shared signature, which dramatically saves space.
Of course, the MuSig addresses must be funded by people on L1 who want to use Ephemeral Settlements. My anticipation is that the less savvy users like those closed-source wallets, exchanges, PayPal and others will be making their bitcoin addresses exclusively on the Ephemeral Settlements layer instead of directly on Layer 1. The underlying exchange/service will then make one giant (in terms of money) transaction to one of these MuSig addresses. This brings two conclusions:
1) The amount of funding transactions to Ephemeral Settlement MuSig addresses are expected to go down over time as people stay on Ephemeral Settlements layer.
2) Exchange and payment processing software will be much simplified as they no longer have to create and maintain their own "virtual reality" of addresses and transactions outside Layer 1.
Come to think of it, I should really post all this to bitcoin-dev mailing list...
Then you need a single transaction for every output to recombine them into a new pool.
And we're back to square one.