See if you like this, Bitcoin as an authentication mechanism:

You have a utxo in an address you control.

A gateway, preprogrammed with that address as your identity, gives you a challenge token and you sign it with that address' keys.

Or, if for whatever reason, you can't send a signed message to the gateway, it can be preprogrammed with your xpub as your identity. You obtain a challenge token and put it in a transaction that moves that utxo to the next address in your xpub, it gets mined in a block, and you obtain access via the gateway.

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Discussion

Wouldn't this be possible without moving the utxo and by simply signing a message?

That's the first scenario, yes.