I have never really worked in a team where there's a designated "Game Designer", so my view could be a bit uninformed.
I have worked, however, in a small team where there's a specific designer, such as a Level Designer, or an Enemy Designer. They are not idea guys. They need actual scripting/programming skills to make levels, or actually able to draw to make enemies. They don't just pull ideas out of thin air, write docs, and get all the credits.
In a non-gaming professional setting, which I am now, there's probably the equivalent of a Game Designer, and that is a Product Manager, a person who foresees the conception of a product. I personally think that a Product Manager is a useless and bloated job that a company can ever have. Although, in a large company that employs more than a couple dozens people, it's kind-of needed to have somebody to run around writing and passing documentations around so that everyone is working and understanding the same thing, and not deviate from the original plan. However, in this case, he's not really the idea guy, but merely somebody in the middle of the communication web.
Can an Idea Guy be part of a team? Yes, but usually somebody with enough power or money or connections (i.e. the CEO). He will start the project with the initial plan, but this is just the skeleton. Then the rest of the team takes it from there and added the meat, the skin, and the polish till the release of the product. Of course, the question if all the credits should be given to the CEO or the team really depends on the company's culture. Minecraft creator, Markus Perrsson, gave a whopping $3 million to the Minecraft's team because he knows, that without the team, Minecraft wouldn't be where it is today. Other companies may not be so, and some greedy CEO might say "Yeah, I created that!", and took all the credits and bonuses.
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