Reports should be limited and renewed weekly or Monthly.
It is my opinion that unlimited reports render the reporting system almosty useless for a number of reasons:
New or inexperienced players are unnecessarity reported. Trolls, smurfs, cheaters, boosters etc slip through the cracks as there are simply too many reports to go through daily.
Let's say everyone had 2 to 4 reports per week, then people would be compelled to work together versus giving up and sending in a report hoping for a solution.
Also, people with think twice before wasting a report card and instead using it when absolutely necessasy.
Also, on it's part, Riot would take more time looking at reports and actually doing some thing about it.