Roman numerals are fine when you want an impressive looking date stamped on to something, but I can't figure out how Romans got to be so good at engineering, as well as census and tax records, when their number system was so ungainly, and not at all easily lent to doing calculations. Then add in the fact that they had no 0, which would prohibit any serious mathematical development.
You are projecting modern biases onto the Romans. If you are used to the Roman numerals it's not hard to do calculations with them, certainly not in the way the Romans used them, with up to 4 I's:
I, II, III, IIII,
V, VI, VII, VIII, VIIII,
X, XI, XII, XIII, XIIII,
XV, XVI, etc.
It's quite simple really. Add I's until you make more than 4, then change the symbol preceding it.
That not having a 0 "prohibits serious mathematical development", seems teleological to me (and to be clear: teleology in history is a bad thing). You're basically calling the Roman number system backward, ignoring the fact that we've had some 2000 odd years of extra development, and ignoring the fact that the Romans used their numbers for other stuff than we do (for instance they didn't need to run computers or particle colliders).
By the way, I don't even know whether or not the Romans had a symbol or concept of "0". They managed some pretty impressive engineering projects regardless.
You are correct that Roman numerals are more unwieldy for calculation than Arabic numerals, but you are forgetting that calculations don't need to be done using numerals: Romans used Roman abacus for calculations, that enabled them to calculate quickly and only use numerals to write down the results.
Regarding specifically division that you ask about, I'm afraid I don't have an exact source for this, but it is my understanding that, since division is a more difficult form of calculation, people went the other way around, and instead of trying to precisely divide any number, they tended to more commonly use numbers that enabled for easier division: hence why dozen was more used than it is today, or why coin values were denominated in powers of two.