There are definitely cases where it's clear what we (as browsers) are supposed to do, but some implementations have chosen to err on the side of user preference rather than correctness. I hope we can move that needle back towards "implement the specs". There's no good reason for any 601- or 709-marked content to display incorrectly in the year 2021.
Unfortunately, if you don't mark the videos, that's on you though. Fwiw Firefox generally does follow Chrome in inferring unmarked bt601/709 based on size: https://searchfox.org/mozilla-central/rev/1df3b4b4d27d413675...
Honestly I would rather issue warnings in these cases rather than silently guess.