My guess would actually be, believe it or not, for clarity. In some typefaces different numbers can look the same (5 and 6 for example could be mistaken for each other). With Roman Numerals there is less confusion as similar letters aren't used, as far as I know (so no IN being mistaken for W or anything like that). Book publishing uses Roman Numerals for copyright dates, so its use in film and TV programmes may be an extension of that convention.
I have to say, I've never had problems understanding Roman Numerals and worked them out in the 1970s by looking up the dates in the Annuals that I had.