Polite forms certainly are irregular. They use old conjugation patterns that aren’t in common use today.
The negative of ～ます is ～ません. In modern Japanese it would have been conjugated as ～まさない.
The negative of です is ではありません which you get by converting to casual form ではない and then turning the ない back to negative polite form ありません.
The word ください is an archaic way of conjugating the verb くださる which you won’t see applied to any other verbs.
It is totally possible to get to useful speaking ability with study in, say, a classroom environment that’s working through things based on a textbook. You don’t even need three years to do it, one would suffice if it’s full time study, and you can get to doing actually useful things with that basic and growing ability as you go along.
Seems to me if you learn a bunch of plain form verbs first you’d end up in a situation where for all Godan verbs you’d have to question if it was godan or ichidan. That is if you learn たべる there’s no hard fast word for you to know it’s たべます and not たべります. There’ll still always be a couple tricky ones though like おります and かります. If you learn them for you’re equally clueless if it’s ichidan or godan, and in all likelihood going to guess them incorrectly. Still seems like slightly less to relearn/ memorize if you do polite first. Idk
It’s true that it’s not automatically clear whether any given -る ending verb is Ichidan or Godan, but you can use some of the verb’s plain transformations to help you remember. Just like how you can make note of the -ます form of a verb to help remember whether it’s Ichidan or Godan, you can use the plain -た and -て forms in the same way since those transformations also differ between Ichidan and Godan.
Not only self study, but schools provide these books most of the time. I wouldn’t call genki an academic resource, it’s a textbook for beginners. 
Just because they enroll in a class because they want to learn something before they go to Japan (most common reason for people to learn Japanese that I’m seeing lately, even if they like anime and stuff) doesn’t mean they’ll stick to it.
What do you mean by this?
You know, this makes me wonder just how much a person’s reason for learning Japanese impacts how they approach learning the language. If you’re making a trip to Japan, you’re probably going to be in a hurry to get to some level of useful polite speaking so starting with polite grammar makes sense and will likely get you by, but then after your trip your motivation dissipates and you drop off.
Whereas if you’re someone like me who’s learning primarily for the sake of reading manga and other written Japanese media, have no particular deadline, and want it to be a lasting skill since you can always find more stuff to read, you might take things more slowly and go for a more methodical approach. Hence why I opted to learn fundamentals with the basic verb forms first and then later look at です/ます with the understanding that they’re just a polite copula and just another helper verb, respectively, not some bizarre things that are in their own unique category. And so that might be the reason I personally found it a bit strange that polite form is like the first thing you see when learning Japanese, but in practice I guess it just works out for most people.
If we’re only talking about the reasons people quit, while people who want to go to Japan stop after their trip because they already reached their objective, most people who want to read manga or watch anime stop when they understand how hard it is and how long it’ll take them, as long as they don’t just fail at keeping up at the start and drop out after their first class. Also, it sets in how learning a language because you like anime and manga (that you can experience in your native language anyway, at least with subtitles) might not be the best decision or use of your time.
Unless it becomes an interest in the language or the culture itself, you don’t end up getting too far. That’s at least the experience of my friends and I.
If everything you ever wanted to read or watch was available in your native language or had subtitles, that might be the case, but not everything made in Japanese ever gets translated to other languages.
I mean, I guess if you want to triple the memory work and memorize the past tense and て form of plain verbs? If you know they’re ichidan (as you usually do with polite verbs) from the start you don’t have to memorize extra forms.
It’s honestly not a big deal either way. Basic forms of the Japanese verb are easy and don’t take that long to learn in the grand scheme of things. You can get both polite and plain done relatively quickly, making my original point not that valuable. Still, if I were to introduce them to someone in an order I’d do polite first as it seems clearly to have less memory “grunt” work. Also you’re unlikely to do any serious reading, speaking, or whatever in your first couple weeks to a month where you learn all those basic verb and adjective forms. You gotta learn all the basic forms kinda quick anyway, so why not take the path of least resistance and do polite first?
Of course, but we all know the majority of people who watch anime aren’t worried about watching an unknown 80s anime movie that was released on a VHS and the only known copy is in the basement of a guy with a YouTube channel where it’s available without subtitles in 480p.
And for the remaining minority of those people, the more obscure stuff that never got translated may indeed be enough to motivate them. You never know. 
Idk, even though my interest is mainly reading, I have developed something of an interest in the language/culture itself that has likely helped keep me interested enough to not completely give up studies after starting several months ago, even though I’ve had times where I had to pause due to other commitments. After taking a long unintended hiatus from Wanikani and resetting to level 1 to start fresh, I took the opportunity to set up a more regular study schedule to try and follow from now on so maybe I’ll learn at a more consistent (even if it’s kind of slow) pace.
But this is veering into “what motivation is good motivation” territory, where your mileage may vary.
Looking forward to seeing you here in 2 years, then. 
That wasn’t really the point I was going for, more like, thinking about how different the paths we’ve taken were, and how important Japanese is in my daily life now when I didn’t really show much promise in my classes
Yeah, but outside of the historical context, the inflections for a given verb a standard across the board except for the actual irregular verbs. Going from 食べる to 食べます works for any ichidan verb.
And if we’re talking about conjugations of the stems themselves, all of that is way less complicated than い-adjectives. 
Plus, you don’t really get all that until later. It’s mostly going to be set phrases.
Samurai form: これは本でござる
I managed to make a whole year fly by in Wanikani getting to level 27 before I fell off the wagon and decided to start over, so who knows, 2 more will probably go by relatively quickly as I’m getting caught back up and studying more grammar on the side.
Well, uncommon, but not unique. いってらっしゃい, for example, comes from いらっしゃる. And all of that bunch of formal verbs change ～る to ～い when changing to the ます form. くださる → くださいます, なさる → なさいます and so forth.
Why would it be まさない? ます is not a verb, so why would you expect it to conjugate like a verb? Some auxiliaries do conjugate like verbs (e.g. られる), but most don’t.
Isn’t all that from である? I don’t think ではありません or ではない or any of that is related to です.
To be fair, beginners just need to know “say ください to be polite”. They don’t have to learn its origin or general-purpose usage for a while.
It’s often the case that the most common / beginner stuff is also the most irregular. Should beginners not learn おはよう because it’s an “irregular” conjugation of 早い? No, they simply learn it as a set phrase and move on until they reach a higher level.
By the way, there are several verbs that work the same way, so it’s not correct to say this is never applied to any other verbs. Off the top of my head:
I do wish people would stop saying that outside of the two main verb classes there are only 2 irregular verbs (する and くる) though. Yes, する and くる are nuts, but there are a bunch of verbs that don’t neatly obey the rules of the main classes.
Even in things as common as 行く, which would be 行いて or 行いた if conjugated by normal く verb rules.
I’m not sure what would be a better way to put it, but the common way of framing it gives a false impression.