I agree, on the past I had a proposal that the OS should have a device level API to provide this information, in this case apps and (the browser as an APP) would be able to consume this information from the device. And it's up to the device manufacturer (or the OS installed) to add a age system.
I not denying that there is holes in this idea. Linux users could simply add a simple form with "I was born 01-01-1900" and everything would continue the same. But on the MicroSlop, Gargle and iPear worlds, they would be able to validate once and keep the information on the device. And each webpage, app and such won't be able to ingest your personal/private data.
On this post, I do explore little bit this, but I do focus on the idea of storage and access of data.