Hmmm... US ~600 ship and large-boat navy, for a population in the half-billion range (acknowledging that the US Census is low by design, being only those counted by census personnel and/or responding on paper... and thus missing most illegals, many legal-but-paranoids, and some legitimate above-boards. (I wasn't counted in the 1990 US Census... Mom and Dad didn't list me cause they thought I'd be listed in the dorms; the dorm staff sent out a memo to have us have our parents count us... cause they didn't have the staff to do so.)
Soo... 1 ship per approximately 1 million people... that puts most of the smaller worlds with one warship or several cutters...
I don't see the problem, Hans. Yes, a few worlds will support up to 10K ship fleets... there's your source for the Imperial Navy support chain....
Seriously, tho', I suspect that the ratios for space navy can and should be lower for the high-pops than for the lower ones, and low pops should also have smaller ships... IMTU, less than 1% of people ever leave their homeworld, and the fraction inches down as the pop increases (and thus likely so does the service industry base available). A million plus people should be able to be fairly self-sufficient; 10 million more so, etc.... a mass exodus from a hive world should be a notable event, not a steady flow. On some small backwaters, perhaps 90 to even 100 percent might have left planet... but the only reasons to leave a garden world like Regina are adventure, civic duty, and work... and those not seeking to do so for adventure and civic duty are unlikely to take the jobs that require leaving anyway.
Some chap on the radio the other day was complaining about the "massive waste of money on space." I know more of that ilk than of the "Why are we wasting money rebuilding Iraq" ilk. Now, go someplace ugly like Kupariq, and Mars doesn't look so bad...
(Kupariq is above the arctic circle, and is pretty much nothing but oil industry... and tundra.)