Stuck in L1?

Do I need to worry about my Ether and so forth getting "stuck" in L1 in the sense that, some day L2's might be where all the action happens, and L1 is a "settlement layer" and therefor very (more so) expensive to move in or out of?

I can imagine a world where the cost of transactions on L1 just keep going up, because it's the big, expensive "commercial" highway the L2's use and therefor is expensive…to the point where moving Ether out becomes (maybe) prohibitively expensive.

No? I hope not also.