I'll need to read again to understand this. So far it seems that LN channels consolidates a lot of transactions and later send them to the main net.
I associate this concept to a train: a lot of people get on the train (LN channel). When the train is full it goes to the main rail (main net). There is no sense to transport only one passenger on the train. If that is the case, then the passenger can use the rail by himself (Not using LN channel).
On the other hand, I'm afraid that a layer 3 blocks access to layer 2. There is some risk that the network becomes centralized. For example, in my country the beaches are public however, to access to some beaches you have to pay because the entry to the beach is private property or natural reserve.
Maybe I'm wrong. Anyway, this is a great post.
This is a little bit technical and I'm a slow, that's why I need to read again :)
layer 3 that are trustless won't need face that problem.
The key layer 3 that are trustless to a certain degree are Statechains and Channel factory(depending the design).
Liquid and RSK are also layer 3 but they are not that trustless or are to a lesser degree ie RSK. RSK is more open than Liquid but still has a Federation which intersting control but doesn't control the bitcoin the same time. RSK does plan to get rid of the Federation but it depends if main net will get a soft fork peg