The value of any given idea is really low - I would argue that for many organisations ideas even have a negative value on average, because you are going to spend a lot of time dealing with the idea without it actually becoming something that generate value in the end.
Even if you have an idea, that works, and that will generate significant value if realised, until that idea IS realised, it is a negative cost.
People who can generate a large amount of those ideas are a commodity.
People who can cheaply identify an idea that can be realised and that have access to resources to realise it, and that can go through the process of actually realising the idea are not a commodity.
The bottle neck for putting new ideas to market is not the idea generation, and so the people who consider themselves "always starters" is not a scarce resource, hence I dont need to rotate them from department to department - every department I have already have access to more than enough good ideas, so adding the "always starter" to that department would be a negative cost.