Still the fee is quite high and not suitable for smaller payments, since the spammers found a way to abuse the mempool with inscriptions, is it really possible for them to be moved to L2 layer which is the only hope right now to keep the blockchain unable for every transaction.
If I understand you correctly, then I suppose you are asking a question, so my answer would be that "I don't know, but then, I do not think it's possible", if it was, I believe someone in the bitcoin blockchain #DevelopmentTeam who also feel bad for the high transaction fees would have suggested this idea.
I mean, taking ethereum as an example, we have several EVM compatible blockchains running as layer 2 of Ethereum, completely independent on the ethereum blockchain, this move or ability have eased what would have been a heavy network load on the ethereum blockchain.
If it was possible for ordinals and inscriptions to build a layer 2 blockchain that is supported by bitcoin but completely independent on the bitcoin network, this would have been a good thing to do, and sure would easy the constant mempool congestion on the bitcoin network.
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I also would love to see those ordinal/runes using a Layer 2 solution.
however, there aren't any decent layer 2 in bitcoin right now. Maybe the best one is Liquid?
I think Lightning Network has very serious User Interface issues, and it is very hard to use.
Maybe those ordinals will speed up L2 solutions