The TLDR appears to be that Alice and a kinda-trusted intermediary referred to as a "Statechain Entity" (SE) fund a timelocked multisig address. Alice can then open channels by creating more timelocked transactions which spend from that address.
Ultimately, Bob trusts that the SE and Alice do not collude, or that the SE and Alice are not the same person.
This seems like the primary drawback. If the Statechain Entity colludes with Alice, she can steal back the money from Bob, or sweep the entire balance of a channel created from the 'peg-out' transaction.
The lightning channel will be timelocked.
If you can't close the channel until the peg-out timelock expires, how can the channel be used to make PTLC or HTLC payments? If an HTLC has a refund time that is earlier than the peg-out transaction's nLockTime, the payment path of the HTLC wouldn't be enforceable. The protocol depends on the SE being online and cooperative to support a force closure. The SE could therefore extort a payee: "Give us x satoshis, or we won't let you redeem your payment."
Cool idea in principle, but in practice it would place way too much trust in the trusted intermediary.
nLockTime, the payment path of the HTLC wouldn't be enforceable. The protocol depends on the SE being online and cooperative to support a force closure. The SE could therefore extort a payee: "Give usxsatoshis, or we won't let you redeem your payment."