See, I think this is the fundamental disconnect in this conversation: I think almost everyone in this thread is in agreement on that fact. The problem is that people aren't really in agreement on what "accessible by the base client" means.
Mini Cactpot Solver stuff isn't reading anything the player doesn't see; it can just see "There's a 5 in this square, which means this row and this column can only be these combinations. If you check the number in one of these three squares, we can see where a high-value line is likely to be." It doesn't see what's behind the scratch-off stuff (because the client doesn't know), and I can do the same math with a pencil and paper (or using a website). Does "a mod that marks which ones I should pick one of to see where the high-value row is likely to be" count as fundamentally different than a website a Playstation player can open on their laptop or smartphone that does the same thing? It's more convenient, but I'm not sure it's fundamentally different.
Cactbot's Raidboss callouts can be faster than a human (in some cases, or way worse in others), but generally speaking I've yet to see Cactbot able to call something I-as-a-raid-caller cannot. Yeah, it could hypothetically call out, say, your specific debuffs for E12S's Intermediate Relativity and such, which is harder for a raid-caller to personalize, but given that those are set patterns I could still call out "DPS have flare, get the hell out". In P1S, I've run with someone learning the fight who had trouble reading where they needed to be, so I just added calling their temperature resolution to the general callout, like, "Alright, resolve your squares. <X>, you'll want to head south." (Which, from what I've been told, is better than what Cactbot calls there anyway, as it will tell you to resolve the second hit in a way that may get you killed on the third.)
Hence why I say that I don't think that on balance, Cactbot gives any meaningful overall advantage to having a human raid-caller.
Stuff that does things like mark invisible AoEs on the ground for you, or lets you ignore debuffs inflicted on you in PvP, and stuff like that? Things which give you capabilities that are, as you put it, beyond those exposed by the base game? I agree those are an issue. I think everyone in this thread agrees those are an issue. (Or anyone who doesn't is probably not saying much.)
XIValexander is the one thing that's been explicitly named in this thread that I honestly have qualms with, as I find myself dithering on it. I've watched friends with terrible ping try to play weaving-heavy jobs and fail due to technical limitations rather than limitations of skill, so I can definitely see the appeal of something that uses the animation lock system to basically try to negate/counteract bad ping. But it could also absolutely be used to cheat, and I'm not sure "functioning on the honor system" is a great approach here. (Though, again, one assumes that if your weaving falls outside of what's actually rationally possible, the server can and will flag it as suspicious. And if it doesn't do that, it ought to.)
Mind you, I think Square-Enix should add that animation-lock-reduced-by-ping-time functionality to the base game, as it would be a great counter to terrible ping. I don't think they will, because glancing at the code for XIValexander suggests that while it would be pretty easy to implement in the client on Windows, it would probably not work well inside the Crossover bottle on Mac and might be a headache to do on Playstation. And SE has demonstrated an understandable (if sometimes annoying) reluctance to implement something on one platform that it cannot readily put into all of them.
At any rate, like I said: I think the reason people are arguing in circles in this thread is not so much that half of the people think "yes I should be allowed to cheat" but rather that people are going "it is unfair when people can use tools to get access to information I don't have", while the other half is going, "Sure, we agree, but the particular tools named don't do that (with maybe the exception of XIValexander, which doesn't give you information you don't otherwise have but does definitely modify the game experience in a more substantial way). They take information you do have and just package it in a more-easily-processed form."
Now, if the argument is "it feels unfair that people can add better accessibility/QoL options to the game on PC when that's denied to console players", yeah, I think a lot of us can get behind that; it does feel like it isn't an equitable situation between the two. It sucks that a PC user can, say, load in a mod that makes the buffs/debuffs you put onto a target displayed with their icons larger than the rest, meaning you can tell at a glance "is that Higanbana on the boss that's about to expire mine, or is it the other SAM's?" and that a Playstation user does not have that option.
There's basically nothing Cactbot can call that I as a raid-caller can't, and I feel like the places it has advantages over me are countered by the parts that it does way worse. But yes, it does still feel unfair in some ways inasmuch as someone who's in a PUG without voice-chat still has a raid-caller (more or less) if they're using Cactbot, whereas if you're on Playstation and venture into PF without your static's raid-caller you're on your own for a read of mechanics.
But if the argument is that QoL changes to repackage information you do have in a more-easily-processed form is cheating... I think that's where folks are disagreeing with each other. Because something can be unfair without being cheating; I think we'd all agree it's unfair that someone who lives in San Jose will have an easier time playing NIN -- personal skill aside -- than someone who lives somewhere in Argentina, simply by virtue of ping and how this game's netcode works. (Or, frankly, an easier time than even someone who lives in like... Philadelphia.)
But I don't think any of us would qualify "I live in San Jose" as meaning that person is cheating, even if it's still unfair.
(And I think I've probably been wordy enough for this thread for... uh, a while. Especially since this is apparently giving my phone's autocorrect an aneurysm.)