What if all transactions are off-chain in Bitcoin?
I agree that a future could emerge in which most payments will be handled offchain. Whenever you want to pay someone and it can't be done via lightning you could just open a payment channel for that amount and keep it open. I also assume cheating won't be too much of an issue and people have strong incentives to keep channels open as the bitcoin are much more liquid on there.
However channel openings and closing will still be a thing thus the bitcoin base layer won't become obsolete and still needs to be maintained. Also some rebalancing is not possible off-chain.
I think in the scenario the bitcoin base layer becomes the institution enforcing the rules of the Lightning Network but it will just be too expensive to do transactions regularly on the baselayer.