The use case for the additional L1 which I have in mind is that is should be fast & cheap to send, scalable, and highly user-friendly to self-custody. So obviously not ETH. The idea is that a L1 with the properties which I just described could work in tandem with BTC to provide a better solution than any BTC + L2 solution.
Discussion
From my understanding you could "bridge" Bitcoin to another L1, but it's always a half baked solution, since you give over custody to get an IOU on the other L1 with no way to enforce the IOU or exit without trusting the custodian, like we see with wrapped Bitcoin.
Then you might as well just use a federated model like fedi or liquid, at least you're distributing the custody risk across multiple custodians.
So far I haven't seen anything that can hit all the requirements you list above, something has always gotta give in the trade off
Is bridging the same or different from simply exchanging the BTC for the L1? Obviously, the L1 needs to have sound tokenomics. However, it isn't possible to even carry out that due diligence if one takes the view that all other L1s are shitcoins. Which is ironic, given that viewpoint may confine you to custodial L2 solutions, at least in terms of realistic mass adoption.