Assuming an engineer did decide where to locate the booth, he/she did not necessarily have to be a traffic engineer. Many civil engineers dabble in secondary areas of expertise -- whether as the designer or reviewer.
Q1: How long has the booth been there? Where was it previously?
Q2: Since you are very familiar with the area, how do you think it could/should have been done differently?
The booth was moved from a location farther inside the park which was suboptimal for other reasons but at least allowed plenty of queuing area on a straight flat section of road. Since considerable work was done adding the bike path and adjusting the road and parking area, the new booth could have equally easily been placed elsewhere. If and when I write up a comment / proposal for the park director, I'll share. There's a (to me) obvious solution that could have been included in the construction at no additional cost / effort, but now will require widening a short section of pavement to accommodate the booth.
(to head off your question: I say "no additional cost" because the wider pavement where they put the booth would no longer be needed, so the same total amount of pavement on similar flat base could have worked in either spot.)
I wasn't really thinking about cost.
Couldn't they have scrapped the booth altogether, and just had some paystations at which to buy permits? Can people with annual permits bypass the booth?
They've never done any kind of untended pay station. And issues such as county residents getting a free annual permit add some complexity to doing that. Those with annuals unfortunately have to wait in the line until they can be waved through; there's no bypass lane.
Sounds like their entire fee program could use an overhaul...
Are the annual (free) permits windshield stickers?