GDP is total economic output per year, not total government budget per year. I don't have to tell you which is larger, or what 10% of GDP looks like in a government budget.
Governments would also not spend 10% of their budget on hunters. Why would you do this when you can spend 10% of your budget on the military on top of what you already spend on them?
I think you are grossly over-estimating the power and revenue stream of the Bounty Hunters Guild. They may be rich, merc work is paid well, but it's not paid so well as to create huge assets like a battleship or even a cruiser. How would they be financed? What kind of financing model would be used to pry the credits out of the hands of the bounty hunters that earn them? Is it an investment for hunters, or do they give part of their earnings as commission? If they give earnings as commission, how much do they give?
There's a lot of work for bounty hunters. But if there's so much work that you can create a fully equipped fleet from the earnings, why not privatise the military organisations instead? Liberty already started moving down that road with the LPI ...
That said, I agree with Joe on almost all counts. I see the RPC being an overall good thing, because in my mind, the Unioners in particular are likely to be organised and skilled enough to maintain them. Perhaps not with the stupid interhouse wars ruining their lucrative trade interception routes in Hudson and Bering but thats a different discussion.