Well, you can try and then you'll appreciate the difference, I am sure. Even if implemented in computer hardware, operating with Roman numerals would either be slow or take many more transistors (or both). As to why in a philosophical sense, it is because the positional system was invented specifically as a computational device, which only happened many years after people learned how write numbers down. Optimization effort takes time, and a random solution is not guaranteed to be optimally suited for a particular application (such as performing calculations).
We all do the same thing. Our calculators work in binary, and we only do i/o in decimal. Their calculators (slaves who pushed pebbles, calculi, around) worked in a decimal place-value system (or used egyptian/russian peasant multiplication), and only the i/o was done in roman numerals.
Sure, but the essence of the discovery, which is in fact far from trivial, is that it was found possible to perform calculations by manipulating written symbols themselves (i.e words) rather than using pebbles or an abacus. (This is by the way how mathematical notation began - as the means of reasoning by performing formal manipulations with marks on paper.)
