If you present people with 100 champions, and tell them 20 are meta, I'm guessing a lot of people won't even look at the lower ones. I'm sure some people will still play their favorite, but pushing the meta will change what some people play. It will also almost certainly make people mad when Riot endorses a champion and then turns around and nerfs them.
As for a meta always existing, a meta does always exist, but it is highly subjective. Even if a game was perfectly balanced there would still be a meta, because a meta is based off of what people think is the best, not which character can actually do the most when played optimally.