I don't think BTC's fees are necessarily bound by its spot price, there is no linear relationship at all between these two variables. In fact, demand to transact in the network plays a much bigger role in fees than its spot price, and the price going to a million dollars doesn't mean anyone's getting priced out of transacting.

It can easily cost over 10k sats to send a transaction

That's about a hundred bucks, and it very well may peak beyond that point all the way up to 500 bucks. But this is the beautiful thing about supply and demand: its self-regulating! No one in their right mind is going to keep transacting at those fees. This is why those ridiculous fees are so short-lived. Those historical fee charts shows that these peaks last for about 2 weeks... every 4-year cycle... which segues into the next thing i wanna talk about:

I also don't think we're rushing for a solution to a problem that, standing to reason, will not probably exist, otherwise Bitcoin's backend would already be bloated with nonesense prophylactic code for the mother of all edge cases.