- If Bob breaks the agreement and broadcasts or the transactions accidentally hit the chain then Alice will just withdraw bitcoins from their outputs.
This parts is similar with LN network where dishonest user attempt to broadcast earlier state of channel, which require honest user online 24/7 or use watchtower.
And AFAIK your idea suffer same problem.
The LN user actually only needs to be online once every (time_to_claim_malicious_tx - reaction_time - time_to_reasonably_get_tx_confirmed). If a LN channel is opened such that a person can claim the entire balance of the channel within 36 hours of an old channel state being broadcast, if it takes 1 hour to react, and 5 hours to be certain their tx will be confirmed, the person will need to be online once every 30 hours to protect their funds.
If bob (the owner of the coin) can claim the entire balance from an intermediary tx within 31 days of the tx being confirmed, he will only need to check the blockchain once every 31 days minus 6 hours. He should not use a watchtower the same way LN channels use watchtowers because there are some cases in which he wants the person broadcasting the tx the ability to move the coin to their own address (when the original owner of the coin dies).