I am trying to understand the technology behind LN and similar concepts.
As I understand it, LN is a network of bidirectional channels, which are created with some limited capacity, within which the channel can operate. So, we can have Alice putting 3 coins to the channel and Bob putting 20 coins to the channel and this 3:20 ratio can then change in time with each off-chain payment, until it eventually reach the point where Alice and Bob want to close the channel at some final balance ratio - say 13:10.
This bidirectional concept has some features (or disadvantages) of e.g. requirement to balance the channel (or create a new one) if payments in one direction are more common. Also each such channel connecting two parties needs two on-chain transactions.
Questions: Why do we use channels only between 2 parties? Would it not be possible to have a channel that is formed e.g. by 4 parties, e.g. Alice with 3 coins, Bob with 4 coins, Cecil with 5 coins and Daniel with 6 coins? It should allow Alice to send e.g. 2 coins to Bob, thus modifying the state of the channel from "A3:B4:C5:D6" to "A1:B6:C5:D6" etc.
If this was possible, we could have 2 on-chain transactions to interconnect 4 (or more) entities, so it seems it would be more effective than bidirectional approach. It also seems to me that keeping the channel balanced would be little bit easier than in case of bidirectional case.
Obviously there would be more communication needed for each off-chain transaction within the channel (all parties would probably have to be involved).
So, is there any fundamental problem with having more than 2 entities in one channel? Or is it just that the benefits of having them would not outweigh the additional complexity?