Alice could continue updating the "state" for multiple periods and at some point they can create a double spend that sends the 1BTC input to another one of their addresses invalidating all the previous payments.
And of course, it is possible to use some kind of multisig, instead of sending coins from Alice's account, and then distribute coins from such CoinPool. Then, the first person going on-chain pays all needed fees, and everyone has an incentive to stay off-chain, as long as fees are high.
So, the model should rather look like that:
+------------------------------------------------------+
| 6-of-6 Taproot Multisig 1.00 BTC -> Bob 0.01 BTC |
| Charlie 0.02 BTC |
| Dave 0.03 BTC |
| Elaine 0.04 BTC |
| Frank 0.05 BTC |
| Alice 0.84 BTC |
+------------------------------------------------------+
And then, it is safe. And also, that CoinPool can just detach a single participant:
+----------------------------------------------------------------------+
| 6-of-6 Taproot Multisig 1.00 BTC -> 5-of-5 Taproot Multisig 0.95 BTC |
| Frank 0.04 BTC |
+----------------------------------------------------------------------+
More than that: it can have a tree-like structure, where there are always two outputs, and where updates are logarithmic. And then, the person going on-chain have to pay the fee for doing that. Or, a group can go on-chain to another multisig, and then the whole leaving group pays the fee.
Edit:
The problem with staying off-chain in a second layer is that you want the ability to settle things on chain anytime you want without delay to avoid being scammed.
Well, it is possible to encrypt the penalty transaction, send it to some P2P network in encrypted form, and make it a global watchtower, available 24/7. Then, if anyone will publish the old state of the channel, the network will see that conflicting transaction, and will use that data, to decrypt the penalty transaction, and broadcast it immediately.
And because sidechains were not accepted in the current form, then I think making a sidechain-like wrapper over Lightning Network is better than nothing. If anything, I would rather use any coin with 1:1 peg with Bitcoin, than some altcoin, because altcoins are too volatile.