I don't hate origin characters per se, indeed, I think it's a step forward for games in general to introduce both custom and fixed protagonists. This grants you the benefits of both: you can have very specific tailored story and reactions for your fixed (origin) characters and the freedom/versatility of custom characters. In theory, it's a great system and I hope it evolves into something amazing over the years.
However, this requires massive resources which are completely wasted if the dual system isn't done REALLY well. From what I can tell, it isn't in BG3.
What the OP calls templates, and I "half-origins" or "DA:O-style origins", is something I've been long advocating for. It's the best of two worlds: customizability and extra reactivity. You could have a whole spectrum of those: from something that could be mostly recreated with custom characters, but with extra backstory, to something very specific/"odd" like the oft-suggested custom vampire spawn. Depending on the chosen "half-origin", different things could be locked; only Criminal background (and everything else customizable) for a member of a certain gang, most things locked for a tiefling sage from Sigil or an exiled/runaway ex-Lolth priestess. An extra benefit of this system is that it would likely take less work to make a bunch of these than to make one origin. From what Larian said, BG3 origins are ridiculously content-heavy.
I am, however, against the option to customize existing, fixed origins. This would remove one advantage they have: expanded story and reactivity. Diluting those would make origins completely half-assed.
Regarding (D&D-sense) backgrounds Niara mentioned: I... half-agree. Backgrounds could definitely use more reactivity, but tying custom character backgrounds to specific backstories would remove some of the "custom" from custom characters. It would need to be done very carefully. I respect Larian's reason for removing background dialogue options - though, like I said, I still think something more could be done with backgrounds. Just... carefully and with lots of consideration.