To your question. A PhD can be longer and useful training for government (for example) if you deliberately choose a) a policy-relevant subject and b) to use your time to build skills and knowledge that will help you in that world, as well as differentiate you from (say) other candidates with a Masters. But do think about communication/policy/teamworking skills - you need to make sure you come out of a program able to write clearly (for policy) and prove you can work with others (a crucial element of government).

Academic departments can be sniffy about a candidate for a PhD program who says they are not interested in an academic career. This reflects narrow thinking about the value of research and knowledge. I did get a PhD place and funding some time back despite setting out a preference for a non-academic career. My only specific recommendation to you would be to present yourself as open-minded, interested in both potential academic and non-academic options following a PhD.

Depending on which bit of government you go for, you could also get a salary bump coming in with a PhD instead of a Masters. But that does not compensate for the additional time invested and lost income/seniority.

The only advantage to a PhD over an applied MA is that it gives you better research chops for some of the research positions at IOs, NGOs, or in the federal government. That sounds nice, but the problem is that you'd probably still be better off with an MA in econ or an MPP from a truly top-tier school than a PhD in poli sci for those jobs.

For what it's worth, the marginal value of a PhD over an MA is huge

Get funded, then leave after you complete the requirements for a master's.

All but the most stultifying dissertations (where you're just doing your advisor's work) will not be fun and instead will suck your soul (even if you love the topic--possibly especially if you love the topic).

Get a Master's degree and then apply to the PMF program.

Will Ph.D. programs accept an applicant who doesn't want to pursue a career in academia and says so in their application?

As someone who has been involved with graduate admissions at a top-20 and a top-10, I can say this would be a definite turnoff for us: anyone stating an interest in something other than being an academic was a non-starter. We didn't get many, but when we did I don't recall admitting any.

This might be myopic or parochial on our behalf but that's how it was. The logic is always "do we really want to advise the person and help them work through research ideas for 5--7 years for them to (deliberately) not end up 'using' our efforts to contribute to the field".