Maybe it's because I don't play Ranked, but the number of games I find myself reporting someone in, in a day, is very small. Remove AFK/DCs, and it's practically non-existent.
If I'm anything like the average, adding a report limit is entirely pointless.
OP seems to be worried about spam reporters, and I can't think of any other situation where a limit would even be reached. But you have to realize that spam reporters are very often incorrect, and as such, they take care of themselves. Riot has stated they diminish the value given to reports made by frequent false reporters, so this shouldn't be an issue.