I imagine Fleiska is right. Allowing for refunds because you don't enjoy a champion would take way too much time from Riot's CS team, however nice it might sound. (It would also promote lack of care in purchasing new champions, or an unpredictability in income if they also refunded purchases with Riot Points.)
Try waiting for a champion to be on the free rotation to try them out. New champions are always free their third week on live. (They _could_ change that but it's a pretty safe bet.) In my opinion the people who should be purchasing champions before trying them are those that have real money to spend on Riot Points, have been playing a while (and/or bought the two bundles of 20 champions) and have the IP to spend, or those who know enough about the game (and their own play style) to judge whether or not a champion will most likely mesh really well with how they play.