Yup, that could happen. That's why it's worrisome. @DarthCoin's suggestion is certainly part of the solution -- figuring out how to migrate stuff onto LN ASAP in a sensible way.

I expect other types of solution will arise, such as the emergence of new institutions that make different tradeoffs w/ sovereignty. You can already see it, in some ways that people don't like (e.g., exchanges) and some people generally like (e.g., fedimint) and everything in between (collaborative custody at Unchained, Casa, etc.)