Let's consider the impossibilities here. Florida a fairly large state: 65,000+ square miles, with everyone living at least six hours from some other place in the state (Orlando is the most centrally-located large city). The point is that the driving alone will destroy your vehicle and savings, and it's not like you're going to get to one state park a week, especially as these parks are further and further away from your home base. One park a week for three years, and, hooray, you get a family pass.
Perhaps you're retired and live in an RV. Maybe you could get to two parks a week. Maybe you'll get to all the parks before you die of boredom. Not that state parks aren't beautiful and all, but visiting two a week for nearly two years will make you wonder whether your life has any purpose, besides getting that family pass so that you can visit the same parks again.
The cost might not be impossible. When I did a search of the closest parks to start off my own quest from Jacksonville, here are the fees I'd owe:
Yellow Bluff Fort Historic State Park - Free
Fort George Island Cultural State Park - Free
Little Talbot Island State Park - $5.00 per vehicle.
Pumpkin Hill Creek Preserve State Park - Free
Big Talbot Island State Park - $3 per vehicle
George Crady Bridge Fishing Pier State Park - $2 per person.($8)
Amelia Island State Park - $2.00 per person. ($8)
Fernandina Plaza Historic State Park - Free
Fort Clinch State Park - $6 per vehicle.
Nine parks would be about 1/18th of the way there. We did three of these parks in one day this winter, so they are pretty close to one another. Since I'm not going to do all the searches on the website (the map is terrible), let's just assume the average sampling is what we'd find throughout the state. 9 parks, $30 for my family to go. $30 x 18 = $540
The annual pass is $120. If it took us three years to visit all these parks, then that would be $360. Then we could get a free $120 pass for the fourth year, just in time for us to never want to see another state park ever again. The biggest problem is the time and gas money, once we start having to visit state parks in other parts of the state.
I don't really think anyone with a real job or an actual family is going to get to all 164 state parks. I can't even imagine most people would want to.