You've just described a way of dealing with the issue when it arises: paying the person working on the less sexy project more. This may sometimes be a tool the manager can use, but it isn't always an option. So presume you don't have this tool, or the value of the project is larger than the value of the compensation you can provide.
> It just wouldn't happen then?
You're presuming that the company can perfectly reward people for work, and that every employee believes that they'll be rewarded optimally for work in the company's best interest. I've yet to encounter a company that can accurately reward employees for their performance, and because of that, I've yet to find a company where the employees believe that their performance will be perfectly fairly rated. If you can fix this problem, I'll buy your product.
I agree, this is a political problem. But it doesn't seem to be unavoidable. Perhaps, increase rewards for long-term gains for the company and remove rewards for short-term personal gains? It just wouldn't happen then?
Team failing to meet the objective. I don't see how this is a political problem.