Actually, an idea that would come from a game dev will almost never come from a single person. It would be a group of people working together to develop a concept. And during that time, you actually need to be extremely critical of the other peoples work in your group. Now critical doesn't necessarily mean negative. You just have to be unbiased when assessing the pros and cons of a concept. So even though you will see when a new champion comes out that the idea was lead by "RiotEmployeeX", that's not to say they designed and made the champion from the ground up. They were the leader in a whole team of people who would look at any given part of a concept and see what works and what doesn't work. When you see character developments of some of Riot's characters and you see things like Ziggs started off as a human called 'Ivan, the Mad Bomber', that gives you a good idea of how much an idea changes during development. So if Riot were to see something they liked in a concept, they would take it and then rip it apart, and turn it into something new.
Now, to answer you question: There's any number of reasons why people post to the forums. Riot have been known to take concepts (usually skins) that people have posted in the past. For example, Void Fizz was a champion idea. Braum was inspired by a comic someone posted in the forums of a guy called 'Angus'. Even suggested changes to abilities have come from forum ideas. For example when Sion was relaunched, is ult originally stopped if he hit a champion and killed them. Someone on the forums suggested it would make more sense that if he hit and killed someone he kept going, and Riot liked this and added it.
As for ideas that don't get added, it depends on the kind of person they are. If you want to get into any sort of creative field, you need to learn to be able to take criticism and feedback, and forums are a good place for that. If you aren't able to change your initial idea, any concept will stagnate. You're limiting yourself because you shut out potential ideas that you may not have thought of. I've been very vocal in the past with some people that it's ok to have a bad concept as long as you're willing to learn from what people say. And for the people who think their champion will be introduced? Well, people just like to be idealistic.