Shortages are caused by sticky prices, not supply-chain problems
"manufacturers allocate cars to dealers by formula. " In some of the shoe industry, a retail store must buy a whole set of sizes for a shoe, with two pairs of the popular sizes and only one pair for the less popular sizes. Despite the retail desire to buy maybe 3 or 4 pair of the popular size and none of the less popular size - for some brands, at least, that's not an option the manufacturer allows.
There are probably "ease of operation" based manufacturer internal procedures that are sub-optimal, or maybe only temporarily sub-optimal, and no easy way of changing those procedures.
You're so absolutely correct that there should be more variability it prices to avoid empty shelves - not so unlike disaster price gouging increases.
My guess on not raising wages would be like yours: " they think that the supply of workers is going to increase soon, and they don’t want to raise wages now and then have to try to cut them later. " - but there seems such an obvious workaround: "temporary" Pandemic bonus to increase wages, and higher prices for the available stuff or services. With the easy ability to lower prices of stuff not sold - like XL or XS sizes so often on sale.