There's often a difference between the Lead Designer, and the Producer - they wear different hats.
The Lead Designers job is to try to make sure the game will be as good as possible. It's to hammer out the design document, arrange meetings with coders, art and designers, and keep the 'vision'.
I'd like to be a Lead Designer.
Producers job is to make sure the game ships on time. They arrange lots of meetings, schedule tasks, arrange backup in case something goes wrong, talks to publishers and marketing, do lunches and interviews with VIPs, makes sure the demo gets to magazines and that screen shots are sent to sites on time. They're there with the stick at milestone deadlines.
I'd hate to be a Producer.
And producers and lead designers fight - they are in different worlds...
LD: "It'll be great! We'll have cutting edge expansive AI that dynamically changes depending on the players actions and the phase of the moon!!!"
P: "We don't have time for that, and its risky - use A* like everyone else."
P: "Hey, LD - make sure the demo is bug free and ready by tomorrow, right? Oh, and I need 40 screenshots too."
LD: "But we've not finished the game yet!! There are bugs we need to fix in the main game to hit deadline!! I've no time for..."
P: "No - do it."
But they're both needed. A game without a Producer will never ship, and a game without a Lead Designer will have no vision and stink.
But try to be both, on anything bigger than a very small commercial project, and you won't be able to keep the two aspects from fighting.
P/LD: "I wanna make it good, but do I have time?!"
(And to answer the original question - I'd like to work for myself as a game maker and freelance designer. And pigs could fly me to work every day in my castle in the clouds
.)