I'm sure I have fundamental misunderstandings but also I have a different way of looking at this math:

For any given miner, the chance of finding a block is the same 10 seconds after a new block or 50 minutes later (you are right). However, for ALL miners, some miner would complete a "late" or "second" valid block very quickly. Then once that second (what I'm calling "late") block is found and announced, everyone could go back to looking for the next block.

In reality, this would be opt-in, so not all miners would play this game. Miners who don't would be more likely to win the next block prize, but forego any chance of earning fees in the L2. And those who do participate would be less likely to win the next block (though not impossible), but would potentially earn fees on the L2.

I don't think the value proposition is absent; what they would get if they "win" is the status of earning fees on the L2. These fees would likely be dynamic, so if few miners were early adopters, they would make the highest fees. It would also smooth out their income (of course, most mining is pooled anyway, but this could smooth out the revenue for the pool operator).

I know this is abstract because it isn't a proposal for a specific L2, and would depend entirely on the incentive structure therein.

I also failed to make clear that running an L2S to gain fees would require minimal computation power and wouldn't reduce the miner's ability to mine as usual (they would be doing both). In fact, it's really stupid of me to not point that out from the onset.