ID verification does not increase risks for majority of people. Most people don’t use single use email aliases and thus harmful association can happen for them in any leak of their account data, with or without ID details. It is likely that higher compliance requirements will actually reduce the risk of a leak. And of course, chances that every website doing verification will store your ID are very low. It‘s costly, so it will likely be outsourced to a third party provider specializing in this job (which will be much more secure than doing it with some WordPress plugin or other shitty custom solution).