Not outlines or any other sort of nested system like that. You lose a whole two layers if you get rid of roman numerals. You’d also have to decide on a new numbering system for things like introductory sections of documents–currently, they’re numbered with lowercase Roman numerals. You could switch to an alphabetical system, but it’s a lot harder to remember that “ad” is page 30 than “xxx.”
Oh, and:
I even remember the numbering system from the game Riven. I don’t think it’s any kind of imposition on kids to teach them another very simple numbering system that still has so many applications, both practical and aesthetic.
Jesus, people…calm down. I was just expressing an opinion, for the love of God.
Personally, I would hate to be befuddled every time I saw a basic Roman numeral. I suspect that since most of us have been taught Roman numerals, they are usually sufficiently transparent that we don’t notice how often they appear. If you don’t know them, then whenever you encounter them, you are functionally innumerate. Since it’s easy enough to learn, that’s a good enough reason to learn them.
Yet, that isn’t really the point. Yes, you could whittle math down to just what you’re most likely to actually need in your life – making change, maintaining a budget, simple measurements, planning a trip. Students should get at least this much out of math, I’m sure we can all agree. So, why don’t we just teach a set of the most essential skills and set the kids on their way? For one thing, because that’s not what math is. Math is a an entire world of numbers, logic, order, pattern, shape, chance, time, proportion – all the stuff we’re swimming in all the time. Not knowing math is a kind of blindness.
Math is not a set of known solutions, it’s a set of thinking exercises that teach you to find solutions. And among those exercises, you are asked to think about numbers in more than one way – common symbols, combination of those symbols, objects arranged in patterns, patterns with countable features, a plot of curves, things that are there and things that are not there, how one number compares to another – and among these you are asked to learn a second set of symbols and a second pattern of arranging those symbols to represent numbers.
Roman numerals are just one of a whole array of traditional methods for exercising your mathematical mind. If you don’t give it credit for the understanding you have now, that doesn’t mean it didn’t do its job.
The fact that we’re all wracked with unbridled fury doesn’t change the fact that knowing roman numerals is still useful. Not so much because we’re morally compelled to call the next movie Star Wars Episode VII, but rather because the first movie was called Star Wars Episode IV. The knowledge of roman numbers must be retained or the old stuff’ll stop making sense.
For example, I was curious about when the show I watched last night was made, so I kept an eye out for the copyright date. MCMLXXIX. What the hey? It makes no sense! I am consumed with confusion and as a result thrust into a deep and enduring depression which will ruin my life. Or wait, no, I know how to translate that; it’s 1979. Phew! Dodged a bullet there.
Does this mean I think that “MCMLXXIX” is somehow nicer than “1979”, or that I would have been bothered if they had written “1979” in that space? Nope. Heck, it would probably have been easier to read, give or take the tendency of arabic numerals to start looking like each other on a blurry low-res picture. (Is that a 6? An 8? I can’t tell - suicide is the only option.) But since they did use roman numerals, it’s necessary for us to keep knowing how to read them.
Yup - it’s a way of showing kids that there’s more than one way of showing numbers, alternative methods, alternative ways of thinking, and that’s actually really useful when it comes to learning things like computer coding.
Yup. Some of the uses of roman numerals are historical, but it is useful to be able to understand stuff from the past as well as the present.
There’s one other totally practical reason: when you want to divide things up into sections. Like in plays: Hamlet Act 2 Scene ii. Or just 2ii. With legal documents the subsections often go far beyond what we could manage with 2a, 2b and so on. And then you’d get people asking if that section was 2b or not 2b. 
Anyway, most of the time kids will be taught roman numerals not as part of a predefined lesson but because they ask about them, and that’s because they’re still used in so many contexts. If they were really difficult to learn then they wouldn’t be widely used, but they’re really easy.