Well, it appears there are at least two hills with people dying on them. 
I promise this will be my last reply on this thread.
It sometimes prevents debates from being contentious if one tries to restate the other side’s position.
My understanding of the other "hill's" position:
You feel that using Double-Check to correct typos (and user synonyms?) without marking a review incorrect makes sense because it prevents one or two unnecessary reviews from adding to your overall workload and lets you progress faster. Seeing something marked incorrect and knowing it moved back a stage or two are both an annoyance that can be easily avoided. So why not do so?
Some also feel that other things like lightning mode and 1x1/paired/back-to-back mode that make reviews sessions go faster without losing accuracy are very worthwhile, because we spend so much time on Wanikani no matter what.
Is my understanding fair?
If so, I think the main point of contention is about our attitudes about extra reviews and incorrect answers.
Some value progressing quickly and “efficiently” through the levels more than I do (and that’s okay). I truly understand that many of us want to avoid unnecessary reviews. I wanted to, too, but I’ve learned to change my attitude about reviews (especially after noticing how long many of the level 60s stick around here still doing daily reviews).
It was unnecessarily confrontative for me to ask if the OP’s goal was to read Japanese or get through the levels quickly, but it was a serious question.
My attitude re: reviews and mistakes (thoughts many have seen repeated elsewhere)
Anyone here beyond level three is paying for a service that quizzes you more often on items you find difficult to memorize, and less often on things you find easy. Really, that’s the primary function of the WK SRS.
The scheduling as things progress is intended to quiz you just before you’re likely to forget an item, but the optimal timing is arguable and almost certainly varies from person to person. The main thing is to see early stage items more frequently, and later stage items less often.
The really important thing to realize is that Wanikani only knows you find something difficult if you answer incorrectly!
Incorrect answers are literally the only feedback you provide. It’s human nature to be annoyed at any incorrect answer (legitimate or typo) but the only effect of one is to tell the system to show you the item again sooner.
A small percentage of “unnecessary” reviews definitely won’t hurt anyone’s learning. If you’re overwhelmed with the number of daily reviews, then it’s a different thing entirely, but in my opinion, one should never feel bad about incorrect answers on Wanikani.
I’ve yet to find an item I’m unable to burn with this attitude, though it admittedly sometimes takes several dozen reviews (necessary or unecessary).
I know in my case I sometimes lie to myself about “typos” and “synonyms,” too. Would I really have written とおす rather than とうす for 通す? しょう rather than しょ for 勝? はっくつ instead of はいくつ for 発掘? When I think “oh, that’s just a synonym for what I typed,” was it really? With all the subtle nuance?
We ALL cheat during our reviews in various ways. I reflexively hit “f” to reveal the correct answer on a miss. Sometimes the explanation gives away the other half. Other times I hit enter to reveal the other half of the answer “to check that it’s what I thought” (yeah, right ).
I already have to fight my desire to F-Enter or shift-hover with Yomichan. I don’t want any more temptations to “cheat”! 
We are all here to learn to read Japanese. Most of us don’t care too much whether it takes us one year or five, but we all know (or should) that getting to level 60 doesn’t mean we’re finished learning Japanese.
What road we choose definitely comes down to personal preference.
Responses to specific points
I agree. Dunno if it should be native functionality, but I’m planning to install it expressly for mistake delay.
This is undeniably true. Let’s quantify:
I take about 6 seconds on the slow side to answer an individual reading/meaning question. I typically do about 130 reviews per day. That’s about 1560 or 26 minutes per day answering questions on average (some days a bit more). A typo costs 2 extra reviews or 4 extra reading/meaning questions. If I have a typo 5% of the time (seems a lot) then my 130 reviews and 26 minutes per day goes up to 137 reviews and 28 minutes. (This is completely and obviously wrong, I’ll quantify correctly once I’ve finished my reviews ).
It’s definitely possible I’m not thinking about this correctly, but I don’t think so. Honestly, I think the annoyance with typos comes down to Ego. Humans (even this one!) just hate getting things wrong.
I don’t follow this, I’m afraid. We are discussing typos with entering readings (via romaji to enter kana), but I don’t understand the last bit. Isn’t the whole point of this site learning to read Kanji? That includes both readings and meanings, doesn’t it?
We appear to agree that in the real world typos mean the Kanji you’re looking for won’t show up. At the very least it will take a lot of scrolling to find the one you’re looking for.
As for “you’ll notice and probably correct”: Autocorrect memes and wrong-kanji memes are very much a thing in Japan.
This argument also doesn’t make logical sense to me. The desired kanji not showing up is exactly equivalent to the right kana not show up, isn’t it? Submitting a typo is the problem, not correcting one.
This is precisely the same point as above. “Slowing down” means reviewing what you typed before submitting it, not typing it perfectly without using the backspace key.
My point is that it’s submitting a typo without looking and noticing it that’s the problem, but that it’s still not the end of the world even if that happens.
My point is twofold:
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Even if you’d simply submitted the typo without using Double-check to correct it, you’d see it again sooner than you would have otherwise.
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It would probably be better to look at what you’re typing and correct it to begin prior to submitting instead of depending on Double-check to catch it for you, though I understand the convenience of it.
I don’t think so. The master list is here
Hooray! Someone else who doesn’t mind “unnecessary” reviews! 
I think your best bet is the self-study quiz. You can also launch self-study from the Item Inspector which can be extremely helpful.
I wrote all this to have something to link to in the future. Apologies for the encyclopedia entry.
Peace, everyone. I’m out.