Certainly a possibility, but this is one reason I’d be inclined to believe there will be some significant demand for direct L1 transactions, and a diverse set of L2 layers.
Are you envisioning homogenous L2s, or those more specialized in nature? I envision the latter, which would mean the number that any individual entity is exposed to would be limited.
But your point does highlight the UX implications of too much fragmentation, and it’s a worthwhile consideration
Where's your ETH?
Evenly sprinkled between StarkNet, zkSync, Arbitrum, and the thirty competitors that will pop up in the next few years.