Funny enough. I remember seeing a thread on Era where a native Japanese speaker was insisting that the Japanese R was actually closer to an L, and got a whole bunch of replies from non-natives telling them, nope, it's an R. I think it's important in cases like this to actively keep yourself yourself aware of what is the language proper, what is transliteration convention, what is translation, and so on.
The English alphabet is meant for writing English. Well, I suppose it's actually meant for writing Latin, but for anglophones like myself we'd be interpreting through the lens of the English language. Maybe it's because English is a lingua franca or because it's so heavy on loanwords, but I think we tend to view it as having all the sounds that exist, which is why when we read German words with umlauts we'd tend to just pretend they aren't there. I was in a class years ago with a guy who genuinely didn't understand why you couldn't just write Chinese in normal English and call it a day.
(Completely tangential but related: the tendency to think that a word looks French and therefore should be pronounced like a French loanword.)
Even if L and R or N and M are both wrong, we feel the need some consistency in a transliteration, so we pick one that we stick to. Then we start to think of it as the "proper" spelling, because English words aren't pronounced as they're spelled anymore and if we don't spell things consistently it all descends into chaos, but it's just the letters that we somewhat arbitrarily decided to stick with.
Similar subject. Lately, I've got the sense that I too strongly map out kana to romaji, and forget the place of things in the chart. So I have no problem recognizing ちゃ and じょ when I read them, but I occasionally forgot that ち is on the T row because it's "chi", or I think that SHITSU (しつ) looks like a longer word than INU (いぬ). I've been typing stuff out recently, and in order to compensate for this problem, I'm forcing myself to write ち as "ti", じゃ as "zya", ん always as "nn" and things like that.