On Android, the date picker widget is fiddly to use for selecting distant dates, like date of birth. Not impossible but requires many many taps.
That you’re correctly using html forms won’t quickly lead to browser improvements.. so the result is that users will hate your forms. Users/your customer might possibly even think that you’re to blame, and not $browserVendor.
“This site only uses functionality provided by the HTML spec” is not a useful goal in and of itself. Using the right tool for the job, which might be JavaScript, is always more important.