I wasn't aware of that honor system in LoL. Yeah sounds similar to what I just wrote. But the thing is they could ask, but only you could decide when you want to "spend" your upvote points (and when I say spend, I mean really spend, if you don't have anymore objective based upvotes you would lose those from your current upvote level, so whoever you're upvoting better be worth it!).
Also notice I said "chance". Having more upvote points would not guarantee you access to limited kits, just push you up a bit more in the queue of many newbies that still have to learn how to play. Medals of course, would be simply cosmetic things that you could show off on your profile.
You are right on the possibility of exploiting the system though. What about a combination of both systems? (Interesting, it seems that LoL uses multiple ranking systems for different things)
The thing is, awarding medals based on spent time/points achieved/kills/whatever else can be earned through just playing simply leads to people farming those, and some of them are pretty much based on FPS, ping, luck and the correct alignment of stars and galaxies.
Average score could be a way to find the "most appropriate" people to rank better. But you can't completely ignore kd and W/L ratios. Because there could be some players that have many teampoints earned through spamming bandages/ammo/repairing/spotting etc. but if they waste 100 "tickets" getting those points how good for their team are they really?
The thing is most automated systems can be exploited by statpadding on lower populated servers, and most user-feedback based systems can be exploited through social engineering...
So what games usually do is either make ranks just a sign of time spent playing/statpadding (pretty useless) or get rid of them completely... Which can also work, but if actions don't have any long term repercussions people just resort to trolling and teamkilling...