To answer the title question, yes and no and it's completely contextual. I'm a big Kingdom Hearts buff so I'm going to use Tetsuya Nomura as my example. Now I've done a bit of research on Mr. Nomura so let me explain how he got his start.
First of all Kingdom Hearts is his idea, but do you think Square Enix just hired him out of the blue for his idea? No. He started out at Square doing bug fixes on Final Fantasy 4. And that's not to say he wasn't doing anything before that but ultimately he had no input when he started at Square. Final Fantasy 5 roles around and he gets to do some monster designs, is he the idea guy yet? A little bit, but no. Here comes Final Fantasy 6 and now he's the graphic director. He's starting to get some ideas out there, especially with him conceiving the characters Shadow and Setzer. Final Fantasy 7, he's now head character designer and has a hold on some of the story elements. But still after all this time he doesn't have complete control over the ideas.
Now lets fast forward to 2000. He's been at the company ~10 years now and he gets to be a director of a game. Now what game is that? None other than Kingdom Hearts. Finally after 10 years he's being paid to be the "idea guy" and probably some other roles but who cares right? It's essentially the closest point you get to being paid for your ideas. And even still not everything was his idea. Because guess what, people are going to review it and demand changes. Not to mention it's essentially a requirement to have Disney and Final Fantasy in this game but those aren't necessarily original ideas.
The point I'm trying to make here is that it's not a yes or no that your ideas are worth something. It's more like a scale and your reputation and background are going to adjust that scale. You have to show that your ideas are worth something.
Hell you can be an idea guy without even making a game. Just look at The Witcher series, that was a novel converted into a game. Andrzej Sapkowski indirectly was the "idea guy" for The Witcher games whether he intended to be or not.
Also I have to mention something about your last statement and AAA studios. Those studios were once indie devs too, they had to try plenty of ideas but when they found what worked for them they had to stick with it. I don't have AAA experience but I'm sure one bad original game could seriously injure or even decimate a studio depending on the size. The game industry is ruthless and a player isn't going to give two shits if the developers go under. They'll just keep demanding and someone else will have to fill the shoes.
Indies on the other hand don't have anything to lose and if they are putting it all on the line that's a stupid decision. Not saying it won't work out for them but it's rare.