I am probably going to regret this but...What's wrong with the Berserker that allegedly makes the Zealot a necessary or welcomed change?
My problem with it is multifold.
1. The name Zealot is terrible. As someone else mentioned, it is immediately evocative of a religious type of person...not a raging barbarian.
The name is fine, it's meant to evoke connotations of someone gripped by religious fervor that drives them to incredible martial heights. They're the fanatical crusaders of the D&D gods.
2. Whether it is intended to "mean" this or not, words have meaning. Whether they are trying to "repurpose/reinvent" a new "D&D" meaning for it or not, "I'm going to be a Zealot!" is not a phrase -in any context- anyone should utter... ever.
well...as opposed to what, exactly? saying "I'm going to play a fighter" doesn't make much more sense, since every class will likely see combat. Other classes aren't as egregious, but saying "I'm a cleric" or "I'm a rogue" feels pretty artificial too.
3. I have an issue with the fact that Barbarian -the class- has become soooo freaking narrow that there is only "Rager" or "Shamanic Spirits-related guy." If the archetype is so pigeon-holed that all you can do with it is give 3 flavors of "berserker rage": Berserker, "Battlerager"<eyeroll>, "Zealot"<angry eyeroll> and 3 flavors of "spirits guy" then maybe it's time to acknowledge the Barbarian is a One-trick Pony deserving of simply being consumed as a subclass of Fighter.
Agreed, most of the way. The fighter really also needs a massive overhaul due to its own lack of identity, but the barb needs a refresher as well.
So, yeah, what's the deal with the Berserker that a "Zealot" is more desirable?
Aside from flavor reasons, which do seem to be the crux of your concerns to be fair, the berserker is just a garbage class mechanically. It was saddled with a massive penalty for using its defining class resource, and it's a penalty that none of the other subclasses share. There's a thread you can dig up here on enworld where someone crunched the numbers, and without the exhaustion penalty the berserker is very close to the zealot, with the subclass in the lead switching based on level. When played by RAW, the berserker loses to every other variation of barbarian by a country mile. Hell, they probably lose to a barbarian without a subclass at all, because at least then you can use all your rages!
Wizards of the coast took the cowards route out as usual, and instead of making official changes to address the problem they just released a corrected version down the line by different name, much like the hexblade was a patch to fix bladelocks.