Rage as religious ecstasy makes sense conceptually, and it's pretty on brand with the (dubious) historical accounts of berserker rage. I'm not saying the subcass does the archetype well, but it's not a ridiculous idea. And barbarian archetypes are generally pretty thin; battlerager, storm herald, wild magic, and world tree are all pretty weird and niche. The only subclass that has much thematic resonance is beast, in that it's basically lycanthropy (terianthropy actually).
Religious ecstasy does work conceptually. Indeed the best-done Paladins I've ever seen in a novel were religious berserkers and absolutely incredibly written. However, they weren't "Barbarians", they were Paladins (literally so).
And it is a ridiculous idea to have them as Barbarians - which D&D describes thusly:
People of towns and cities take pride in their settled ways, as if denying one’s connection to nature were a mark of superiority. To a barbarian, though, a settled life is no virtue, but a sign of weakness. The strong embrace nature—valuing keen instincts, primal physicality, and ferocious rage. Barbarians are uncomfortable when hedged in by walls and crowds. They thrive in the wilds of their homelands: the tundra, jungle, or grasslands where their tribes live and hunt.
To have a Paladin subclass which was Berserker-like? That'd be cool and with bolder designers, might even be a thing 5E might see. Further, as you point out, the abilities of the Zealot are just bizarre and don't align particularly well with the concept. They almost feel like someone came up with the mechanics and then tried to justify them with some dubious lore.
As for "niche", well, Battlerager is, but only because WotC chose a lunatic course of trying to make it some kind of weird underpowered Dwarf-specific thing. Battleragers already existed in D&D and were way cool in 4E (actually a Fighter subclass IIRC, but that's fine), but that's just another example of bad design terrified of revealing 4E roots. Storm Herald and World Tree thematically work a lot better than Zealot and mechanically make more sense, albeit World Tree has a couple of bad design choices - at least they're significantly nature/primal connected. Being niche isn't really the problem - making no sense is as a Barbarian subclass is - and that's the problem for Zealot. Wild Magic Barb I have a pretty low opinion of. I have no idea who came up with that, but's illustrative of how WotC has struggled with Barb subclass, because Barb, by their own design, is perhaps narrower than a full-on class should be.
Why does the monk class need to go? It has bad mechanics, sure, but there's lots of fiction and character ideas that a monk class makes possible. The Four Elements monk is awful, sure, but it's not bad to have Avatar style bending represented in the game.
Because it's a specific, singularly 1970s archetype, basically just all the legends of the Shaolin monks crammed together (apparently possibly by way of Remo Williams?), and it's thus terrible at its job of being the "martial artist" class. I mean, we've got three different classes to represent what are broadly "wizards" (Wizard, Sorcerer and Warlock), but instead of even one broad magical martial artist class (an incredibly common archetype in fantasy), we have an ultra-narrow and specific Monk class, just because it's an intentional throw-back for the sake of an apology edition.
You say there's lots of fiction and character ideas it makes possible - I disagree - there's a ton of fiction and character ideas it completely blocks by existing and being so hyper-specific and weird. Countless players want to play magical martial artists, but are completely put off by the Monk's name and vibe and general approach - and D&D 5E offers zero other support for them because Crawford has consistent treated the ability to make unarmed attacks that do more than 1 damage as dangerously powerful for the whole of 5E.
I like the theme that oath of glory serves, but you're right that it fits pretty loosely with the paladin class. It makes a lot of sense in Theros, but not so much otherwise. A lot of these features--like a feature called "living legend"--would make so much more sense on the fighter's champion subclass (instead of its weak, boring, crit-fishing feature).
Exactly - I get why they did it for Theros, but it absolutely should not be a PHB subclass ahead of any other Paladin subclass.
Getting rid of the vanilla ranger would be an interesting direction, which hadn't occurred to me. If they did do that though, I'd want them to replace it with a revised monster hunter subclass, since that's a more universal theme, and since there's a big contemporary fantasy series--the witcher series--which makes that theme more relevant.
Absolutely - that's a fine idea. A Witcher-esque Ranger subclass, given they seem to want to go hard on the magical ranger would make huge sense and probably work decently mechanically.
Maybe assassin doesn't work in 5e. But it'd be a hell of an archetype to leave out.
Could another class do it? Like, rename the gloom stalker to assassin, and lean in to its poweful first strike, disguise self, and invisibility to darkvision.
Certainly the Gloom Stalker Ranger is a much better "assassin" than the Assassin Rogue. But WotC leaves out tons of archetypes, or supports them poorly, so I'd suggest just leaving it out of the PHB entirely given 5E makes assassinations that aren't DM fiat or of such low-HP NPCs that anyone could do it (and any Full Caster or a Warlock could likely do it much, much, much, much better than an Assassin Rogue) just flatly not possible.