Also what the fuck are these moderators doing that they need tools that do more than 100 API calls a minute? Seriously moderating is looking at a post and deciding if you delete or ban the user
The mods are insisting they can't moderate without their favourite third party apps.
I'm (obviously) not a reddit mod, but going off the official website - in the official reddit app, to ban someone you need to have mod mode enabled, then either click on your subreddit mod tab and add them to a list of banned users, or click on their profile and then click to ban them.


Some of the 3rd party apps let you one-click ban people, including without opening the post;


The other main benefits third party apps have are creating a multifeed of modmail (users messaging the mods), mod queue (list of things that have been automoderated for approval or reported) and mod log (list of actions taken by other mods) so if you're moderating a bunch of massive subreddits you've got them all in one place. Likewise there's sometimes some integration with custom bots and other fancy features like highlighting posts from new reddit accounts or gesture control moderator actions (if you pay for Apollo Premium).
Basically only really impacting power tripping mods or the powermods who mod tonnes of subreddits, or who want to do unusual specific features on their phones on the fly like modifying other mods's access permissions easily (which can still be achieved through the browser). I think it's more that the powermods are used to being catered to by the admins, and when the API changes were brought up and the powermods were like "Spez my dude, can you roll this back please? I don't want to switch to the official app" they were confronted at how transactional their "powerful friendships" really were and couldn't handle being told no.
Mods thinking they worth something when in fact they worth nothing contribute to nothing and doing it FOR FREE is fucking hilarious. It reminds me of the BPD ex that tells you "If you leave, you'll never find someone like me" or "If you leave I'll kill myself" but instead it's "if you demod me, you'll never find someone like me who'll do it FOR FREE" and "if you demod me, I'll remove all automod shit". Both sides are shitty, but if Reddit wanted to create automod bots, they certainly have the ability to make anyone else who is willing to do it for free.
It's very BPD, which I guess shouldn't be surprising given the number of terminally online trannies involved (to the point where there's an insane network of tranny powermods that have control over a large number of large subreddits and also most lgbt subreddits, especially including the ones targeted towards lgbt youth; it's how Aimee Challenor got hired, he used to be a powermod who was friends with other powermods, and that's also how he met his paedophile polycule partners).
Reddit has an automoderator built in. It can blacklist keywords, remove highly reported content, assign link flair (like how some subreddits tag things behind a paywall), filter source links, restrict images in comments to users who've got high subreddit-specific karma (so are regular posters), schedule regular posts (like a daily megathread), /r/4chan used it to automatically PM Avengers: Endgame spoilers to anyone who commented...
There's a few features it doesn't have,
which is why third party bots are a thing, for example scanning image submissions with a neural net and automatically removing posts that it thinks are porn, or reading a chain of single letter comments to see if people were spelling out a no-no word. The main feature is automatically banning people (automod doesn't ban). BotDefense does it based on accounts that are frequently reported to it as spam (like those auto-reply bots) but the most popular bots (SaferBot/SafestBot) are the ones that let mods ban anyone from their subreddits if they post in no-no subreddits. This is legitimately a feature that a lot of people have a big issue with, and it has been argued in the past is a breach of mod rules. The mods say it's to combat "brigading".
Reddit argues it has its own features to combat brigading - "crowd control" (auto-collapse comments from non-regular users) and automod rules to remove posts from people who aren't regulars - but the powermods
like auto-banning anyone from wrongthink subreddits either to enforce groupthink or literally just to punish TERFs for daring to TERF or whatever.