Clubs (and race organisers) don't keep the unattached levy - that's a misconception.
As an UKA affiliated club we have to pay £25 for a permit for every road race that we organise. We then have to pay an amount to UKA based on the number of runners that ran in the race and not on the number of unattached runners.
So if we have a race with a few hundred runners, we already have incurred a significant cost.
This system hugely favours the mass races and undoubtedly was cooked up by the London Marathon / Great Run lot - self interest most definitely.
If that applied to each and every Park Run, you would have a fixed overhead for your permit and insurance through UKA of between £50 and £300 per race.
So no - Parkrun isn't treated as an affiliated club in the way that you outline - and your "free" permit and insurance is in effect public funding as the cover comes from UKA.