When you are age-checked in real life, the bouncer glances at your ID, checks the date of birth, checks the photo and lets you through, having not remembered a shred of that information. You are just one in a crowd of a thousand. If you're old enough, they may even wave you through without looking at any real data.
When you're age-checked on the internet, a scan of your ID goes on the website, then is likely forwarded to a helpful third party business. It extracts every bit of data, analyzes your picture, then carefully saves and catalogues everything, and returns True to the website, which may have also stored their own copy of this data, depending on how the process is implemented. This data is now in their hands forever. If, at any point in the future, you access another age-gated website that uses the same third party business, now there's nothing stopping them from correlating that private browsing data. How juicy. Adtech will love that. As you keep handing out your ID left and right, every single bit you divulge is recorded somewhere, forever. And at the end of the day, this is just moving data around, so there's nothing preventing your government, or the host's government, or all governments from passing a law that asks for that data to be shared with them - just in case, you know. Now there's many copies of your exact identity floating around, just one data leak or legal request away from revealing everything you've ever done tied in a neat little package. Real life ID is limited by constraints of practicality and our physical world, digital ID is limited by nothing.
And this is the best-case scenario I'm describing here. Imagine if they ask us to show our identities publicly, not just to the corporate all-seeing-eyes. Everyone would become doxxable by default, their whole life exposed and searchable, the mere idea of having secrets would be wiped away, communities made for marginalized or at-risk people would all fall silent.
Yes, there are ideas about zero-knowledge proofs and legislation about data privacy and whatever else. But these don't benefit either corporations or governments, and the average Joe doesn't care about putting his real name on everything, so we can pretty safely assume that this won't happen.