Sorry, I mistakenly assumed you were talking about disk storage - sure, if you’re designing your own solution, definitely use tags! Although the ones Gmail uses aren’t really portable in my experience, so you’re forced to use their mail client. That, however, is pretty much unavoidable if you’re putting a new spin on established protocols like they’re doing - maybe those changes will get picked up by other clients, maybe they won’t, who knows?
Late reply, but for me personally, I started doing it because my Keepass database is already accessed using two factors (password and key file). Therefore, I’d gain very little by keeping the second factor of those sites external - essentially, those second factors are compounded into the second factor for the database.