The nature of what we consider 'wilderness' has changed significantly in the time the Trail has been around, and the Trail itself has been one catalyst for the change. Remember that when it was first laid out, it did indeed have hundreds of miles of roadwalk, and where it was off-road, it was often on the dirt roads left behind by recent clearcuts, walking through the fireweed and alder thickets of early-succession meadow in newly logged land. It was pretty ugly, and surely not wilderness by any stretch of the imagination. Big pieces of the Poconos, Harriman and the Taconics were industrial wastelands: the Trail is essentially on brownfield there, although nearly a century of abandonment has allowed Nature to reclaim much. Nowadays, our eyes tend to pass over the ruins of industry in the nearly-mature second-growth forest, and we call it 'wilderness' again.
Ir is the experience of wilderness through the National Parks, and through the trails, that has made the public aware that the wilderness has a value, rather than being 'waste' land that is worthless unless developed. If people don't have the ability directly to experience it, they will not learn its value, and they will join the growing chorus in Washington that think that the Government simply needs to sell off our public lands to the highest bidder.
We do love the wilderness to death. It's a delicate balancing act. Putting it on a pedestal where the public has no access will surely kill it. Requiring hard-to-attain credentials before one is granted access will be hardly any better, and making access expensive might even make things worse (a populist politician could then denounce the public lands as rich men's playgrounds).
We somehow need a tiered system of access, with KoA and Jellystone Park at one end, and backcountry permits for multiday bushwhacks at the other. Perhaps BSP belongs higher on that scale than it is. There still needs to be a broadly-accessible path of entry, where those who want to find out for themselves what wilderness is like have a place to do so, without needing first to prove themselves worthy. None of us is worthy, and setting a test is likely to weed out those of us who would be the best advocates - because those individuals are the ones who are already aware that we cannot be worthy, and will stay away.
For all the misbehaviour of A-T hikers, nobody returns from a long hike still believing that time and money spent on preserving the wilderness is time and money wasted. That's at least something. And it's a baby that we must not throw out with the bathwater.
I don't think there are good answers. I expect that in the next few years things will get very ugly.