I don't think this would make receiving harder than just pushing the Receive button. The wallet just has to sign a tx, that's very easy.

As for multisig wallets, it's the same: the devices belonging to the keyholders just do this when they generate their key, and they simply send the result (key+signature) to whoever's making the multisig. The multisig creation software includes the proof with the multisig address. Then whoever wants to send money to them just does what they do currently: scan a qr code or copy-paste the address (which includes the proof), and their wallet does the rest.

A clear downside is that it's harder to make a wallet when every time you make a pubkey you must also sign a message with it. But I don't think that makes it harder for the user, not even a multisig user -- they just click Receive (or Export Multisig Key) and their wallet does everything else.

Addresses would get longer but I'm not sure how significant of a drawback that is.