Will we eventually be able to register ENS on layer 2?

I was reading a few articles about ENS moving to layer 2. (for example https://blog.mycrypto.com/ens-and-layer-2). It seems we might have a good solution to reduce the fee of registering subdomain

But none of them mentioned about the ENS register. So, my question is, based on the current technical status and layer 2 solution, is it possible to move the ENS register to layer 2 to reduce gas fee?

The registration of .eth is done by EthRegistrar, not registry so it is possible to register .eth names on L2 once we migrate the .eth to a specific L2 but that will be after an L2 solution to be proven sound.

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