Part of it's probably an arbitrary number that was suitable a few seasons ago (like still having 3/6 bans), but may or may not be up-to-date.
Another part is probably a server space thing- it used to be stored client-side, but that ended up with people able to give themselves 100% summoner spell cdr (you could set the client to allocate 30 mastery points at once, and it wouldn't respect the '3 point limit' on the 1st level mastery, which was something along the lines of 4-8-12% summoner cdr). So it's on servers now, and when you deal with millions of data sets, storage space is at least a concern (I mean, you'd probably need something along the lines of what... a couple kilo's to get a readable data set for one, x20, x20E6... roughly 80E7 kilo's = 80E4 mega = 800 gigabytes? And that's just for masteries- and it'll continue to grow even without increasing the number of masteries.)
Not a gigantic amount of space, but it's still something. (Also using sketchy estimates- could easily be 2 to ten times that, depending on formatting, encryption, and any number of other concerns.)