Not sure what the issue in your instance may be, because HTML#5 has
been supported in Safari for many years, in Mac OS X. Not sure if it
can 'request' them, or if an official plugin from Apple is needed to be
present so it can be 'set to select' such an option with a new default.
(The youtube flash player is not helpful here because it forces Flash.)
For developers, the section about Safari suggests it is fully capable:
https://developer.apple.com/safari/features/
While I have and use a supported recent version of Safari, my usual
browsers include Firefox 49.x, SeaMonkey (both mozilla code) and
I use both of them more of the time. ~ Also SeaMonkey does email.
Other than the footprint of memory/RAM use, which is higher in Firefox
than Safari, it does OK and has several features plus mozilla add-ons.
Sorry to not be of much help; I'd try Firefox as it has less issues than Chrome
in a modern macOS X. - Chrome can use more system resources than Firefox.
Good luck & happy trails! 🙂