One problem with this framing is that almost any idea interesting enough to base a company around will almost certainly change during the execution. The original idea for Twitter wasn't anywhere near what it became, and you can say the same thing about Facebook, Youtube, or pretty much any of the other Big Things to happen recently (some exceptions of course: PageRank was and is still mostly just PageRank).
Thus, the execution is a central part of the "idea" process. Being an "idea" person without being an "execution" person leaves you open to a bunch of dangers - the biggest one being a sense of inadequacy. If all that you bring to the table is your idea baby, it will be really hard to kill it off and go with something else, even if it's the best decision. So either be good at "adapting" your idea, at times to the point of complete transformation, or start learning to execute.
Thus, the execution is a central part of the "idea" process. Being an "idea" person without being an "execution" person leaves you open to a bunch of dangers - the biggest one being a sense of inadequacy. If all that you bring to the table is your idea baby, it will be really hard to kill it off and go with something else, even if it's the best decision. So either be good at "adapting" your idea, at times to the point of complete transformation, or start learning to execute.