Possible issues I have with this idea (may vary depending on actual execution):
- very easy to manipulate
- if people are required to so something like click on "Like" or "Dislike", you don't know if that's an honest vote or a redirect from the person's blog/YouTube Account/whatever saying "hello, all my subscribers, even if you don't know what this rating system is about, please give me a Thumbs Up!", making the entire system pointless.
- peer pressure when you just want to relax/have fun; I have no problem with people being more friendly than in the past, but it's a hollow, strained happiness and fake smiles - indeed I think it'll make it hard to judge who is honest and who wants a discount. The internet can be a rough sewer, but this roughness is a side-effect of deliberated honesty, something I also value.
- buying things over a shared "goody good person" proxy account should still be possible
- popularity doesn't equal likability and both things cannot be expressed in simple numbers imo
- seems hard to break out of this system, once you get a pretty negative rep nobody will give you a second chance, starting a vicious cycle.
- of course, MASSIVE griefing potential, be it through your own friends, by accident because you thought your little sibling was more well-mannered on the internet than he really is, or because Anonymous or another group of people just dislikes you - so they take revenge by making you pay in the future. That can be because you're behaving like an asshole, that can be because you had the "wrong" opinion among a certain kind of people. Again, that would make the system pointless as people don't judge your playing behavior.
- Expect massive amounts of Dislikes if you're a good player and people ragequit because of you.
...and this is from a guy that mains Medic and Engineer and helps his team despite he'd like to play Spy; but alas, two Spies on a 5-man-team are already too much.
Really, just imagine a 100-member-strong group of people that dislikes this system so much they just leave negative feedback on pretty much any account. I don't think Valve would track every single Like/Dislike or hear both sides for justification or their mailbox would explode, so these events could become possible.