I can't imagine it would be because the contestant couldn't win all the small prizes. You can't win every prize in Any Number. It's also possible to win the car without winning a single small prize in Pathfinder. It's even possible to win more in Money Game with a non-perfect playing than getting the car with just 2 picks (same idea as Pathfinder for a perfect vs non-perfect playing). I'm sure there are other games like this (not sure how Trader Bob awarded the small prizes), but those are a couple that stick out in my mind.
I think there are game's with many more setup complications than loading up a few pairs of small prizes on the turntable.
The gameboard being visible was likely a very minor issue that could have easily been fixed by bringing out the small prizes on wheeled pedestals on the stage floor.
While it may seem like blind guessing to you, there's still the element of pricing as the contestant needed to have an idea of the cost of reach item to know which ones to give and which ones to keep.
Timing is the most likely reason as back then most, if not all, small prizes were still described in more detail. Game explanation/intro, main prize description, 6 small prize descriptions with decisions/banter in between could use up a lot of time. The game wasn't all that exciting to warrant so much time used to play it. It couldn't have been hated that much if they kept it for 18yrs, although I'm sure if you asked people between 1972 and 1990 when the game pool was much smaller what their favorite Pricing Game was, very few people likely said Give or Keep.