How do you evaluate the potential for getting funding of post doc applicants? This answer of mine, in which I advocate listing internal funding of your PhD studies on your CV, is not well liked. When evaluating potential post docs for my lab, I am interested in if the applicant is going to be competitive for external funding. I take self funding a PhD as being an indication that the applicant was unable to obtain external funding. I give applicants who were funded internally by a department or someone else's grant a big pass since the need for external funding was absent. Is the no funding/internal funding distinction important for a potential post doc supervisor to know? If not why?
Do you mean fellowships and other PhD-student only external awards, or are you OK with listing "I helped write this larger project grant that covered lots of people but I was not listed by name in the application"?

I think that in the last couple of years of a PhD, students should be helping to write the project proposals, but there are lots of reasons besides failure and lack of trying that might explain why they did not. Well-funded supervisors may, in my opinion misguidedly, shield their students from grant writing so that they can focus on the research. I think that this is a failure on the part of the supervisor to properly prepare a student for future research work, but it happens all the time. Some people don't get this training until the are a postdoc. You shouldn't hold the actions of the supervisor against the candidate. 

Also, some applicants may believe that if they were "only" part of the writing team but not a co-PI or Senior Personnel (in NSF-speak) on an application, that they should not list it on their CV.

Finally, even for external grants which only cover a single student (fellowships and the like), having not applied for one doesn't mean much. There are many, many more PhD students than there are fellowship opportunities.  

If you are trashing CVs for any of these reasons, you may be missing out on good postdocs.

Edited to answer the question (sort of): I don't hire a lot of postdocs, but I have directly or indirectly hired 20-30 PhD-level research staff. Some of them are expected to participate in proposal writing. We gauge their ability to write proposals by looking for it on CVs, asking them about their experience when it's not on their CVs, and talking about it during interviews. Then, we throw them in the deep end and see what happens. In my organization, we have large-scale projects that fund people's time, but if they want to work on their personal research projects, they need to write proposals. Those who do, get to work on things besides the center-wide projects. Those who don't, don't.