On the surface it seems reasonable to ask for an equivalent ID check online.
But. The bouncer doesn't photocopy my ID and store it in a poorly secured back room that is regularly raided by criminal enterprises or outright sold by unscrupulous owners of the establishment. Similarly, they don't check in with the government in a manner that leaves a record.
I'm fine with an ID check, but I think it is also reasonable to demand the same level of privacy that one gets when visiting a bar, casino, burlesque club, or similar establishment.