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As we know, there are several off-chain solutions called payment channels in Bitcoin. The users can move off-chain their transactions and maintain a local ledger themselves. They only need to turn to the global chain when a dispute happens or some channel is exhausted. And moreover, the payment network can organize the payment channels together so that users with no direct channels can also perform off-chain payment. The network also brings the opportunity to recover the exhausted channels with off-chain method by adjusting the balance among the channels.
So I have the following questions:
(1) Is it possible to move all transactions off-chain? I think it is possible for the following reasons. Firstly, no one will cheat from the perspective of game theory, so no dispute will happen. Secondly, no channel will exhaust with the off-chain recovering method.
(2) If not, what prevents it from happenning?
(3) If it is possible, what if all transactions move off-chain? I can imagine that if no transactions are on the blockchain, the the blockchain will disappear even when it is still exists. We no longer need to maintain it. Then what it brings to this world?

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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.

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