I'll bite.

I think you're right the agency probably didn't sit down, write down definition of fairness, then design a permitting system around it. They probably implemented the cheapest/easiest digital analog they could find to a traditional fax-in/walk-up first-come/first-served permitting system.

However, the intentionality of the implementers was not central to my argument.

The system was created by (probably) non-technical people under a certain set of assumptions: namely, that this digital first-come first-served system would function approximately like the old paper one, but with fewer dead trees and toil. The old one was rate-limited by having to call an office and probably talk to a human, and the assumption that if you call every 5 minutes that human will probably get annoyed with you and stop answering your calls. The new one is rate-limited by the assumption that most campers simply can't spend all day refreshing a website.

The traditional first-come first-served system isn't intrinsically "ethical" or "fair" for some classes of people (as you've astutely pointed out), at best it's a crude approximation of some version of fairness. While crude, it was established by a democratically-elected government tasked with allocating a shared resource. "People who can automate HTTP API calls" and the nearby "people who can hire people to automate HTTP API calls" (as has actually happened with some outdoor permits) were almost certainly not in the groups of people the government was seeking to advantage by choosing this system, and I think most engineers are smart enough to be able to intuit that.

So the root of my comment was this: GP is using special knowledge they have (and probably worked hard for) to extract more of a public good than the public really intended to have access to.

* Is that fair to everyone who doesn't have GP's knowledge? Do people like the GP deserve more camping spots than others? This is a public resource, not sneakers, so fairness is important.
* If everyone with programming knowledge acted the way GP acts, would that maximize the public good?
* If everyone with programming knowledge acted the way GP acts, would the system even function at all?

My answers are basically:
* No. Everyone who wants deserves an equal chance at the spots. If there's more demand than spots, it's the government's job to decide. Random programmers on the internet intentionally subverting the government's intentions is wrong regardless fairness (or lack thereof) of the original system).
It would nearly-minimize the public good. Only programmers and people who can hire them would get popular camping spots. This is a real problem is popular outdoors areas around tech hubs. There's a reason NPS will only accept old-fashioned faxes provably not sent from a free online relay for the most popular Sierras routes in CA (e.g. the JMT and much of Yosemite), and it's not because they want to rock like it's the 80's or because the government is backwards. It's because assholes tried to spam the process with automation. I think some (like Half Dome) were migrated to a new lottery system on outdoor.gov this year.
* The system would completely collapse, and most smart programmers could predict that. The government would have to spend more money on servers just to serve bots pinging the registration system constantly, or it would crash. Even if they did that, the people who gots slots would be a vanishingly small subset of the population (programmers) or people who can hire them. Likely, a grey market for "scalped" permits would arise.