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I think you've hit an important point here. The ability to sign messages with a wallet (which is super simple) brings a ton of other possibilities that could make things like wallet-verified Twitter accounts for combatting bots more viable
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A support to send to an LN addresses.
As for on-chain wallets: except Bluewallet, I don't know about any other mobile, Bitcoin only wallet I can sign messages with.
Also the possibility to connect via Tor is something I'm missing in many wallets.