"No third-party trust: the two peers in a channel pay each other directly using regular Bitcoin transactions (of which only one is broadcast) so at no point does any third party control their funds."
...except they are not exchanging bitcoin.
They are exchanging promissory notes for bitcoin on a platform that has nothing to do with the bitcoin blockchain except that it occasionally attempts to reconcile its position with the asset that backs it.
Monetarily, it's no different from a gold ETF that can get levered up to kingdom come if the powers that happen to be running it see fit to do so.
As I already said - thats what makes the difference between a "bearer token" and a "promissory note".
10,000 year old society already knows all about the Lightning Network. Has already seen it and has already traded it.
If you know that the promise can't be broken because the funds will get transferred when the channel closes, then there is no problem.
The problem is when you have no idea if the promise will be kept. That's not the case here.
Banking = promise where you have no idea if the agreement will be honored.
Payment channel = you know for a fact that the channel can be closed, settling the fund transfer
One is trusted / wishful thinking, the other is trustless and assured algorithmically.