Is writing a grant proposal at the end of Ph.D. a good idea? I will be getting my Ph.D. in computer science in several months, from a US university.

Over the course of my research I have stumbled on a number of interesting directions that I didn't have time to pursue.

Now that my Ph.D. is coming to an end, and I will be leaving (hopefully for a postdoc), I was wondering if it's a good idea to put some of these research directions into a grant proposal with my advisors?

My questions are:


Is this a good idea, especially given the fact that I will not be affiliated with my current institution anymore?
Is this a good career move, at this point, or should I postpone this to another time?
Writing grant proposals with your supervisors is great experience and good for your career.  Writing in partnership with more experienced researchers is a great to to get "apprenticeship" experience and to become introduced to key funding agencies, program managers, and the expectations and practices in interacting with them.  Moreover, even if you move on before the grant is funded, you may find yourself able to work on the project via a subcontract to your new institution or else to help supervise students on the project from afar (I certainly had this experience).  

Thus, if there is a good opportunity for doing collaborating with your supervisors on grant-writing, I highly advise doing so.