Be careful what you wish for. If park football can survive without refs for a week or two why not a season. Remove the need the vast majority of refs. Leave the CFAs to manage no more than 5,000 refs from county upwards. There are about 1,000 level 4's and above, so my estimate is probably not too far off.
The numbers could be culled by more stringent assessment and skills testing. Stop the no lower than 5 demotion for refs who got to a 4, a trapdoor for all. Create a vibrant and fluid promotion ladder.
You'd get a load of refs running games outside the protection of the FA, but no big problem. Charge teams more for participating in the leagues- will make up for lost revenue. Less hassle for CFA, no discipline issues to deal with from the parks.
Jobs a good un-
I wouldn't want this scenario, but it could happen.