Do you know why the laws generally prohibit direct-to-consumer sales...

My understanding is that way back in the beginning of automobiles the manufacturers couldn't afford to build sales and service outlets all over the place so they followed a franchise model. The franchise owners, called dealers, would invest in building a Dealership that bought vehicles from the manufacturer and then resell them to customers, when those vehicles broke they would fix (service) them.

After a while the auto manufacturers built up enough money and started building their own Dealerships but that put them in direct competition with the existing Franchise Dealerships. It also put their existing Franchise Dealerships at a competitive disadvantage because vehicles at their own Dealerships didn't have the markup on them like the ones the Franchise Dealerships were forced to purchase. In many places the Auto Makers didn't want to do Service either, they just wanted to open Showrooms and do Sales.

So the Franchise Dealerships went to their State Legislatures and had them pass laws so that the Auto Manufacturers couldn't open their own Dealerships or sell directly to consumers. It was, and is, protectionism but it makes a certain amount of sense from both the Franchise Dealership and Consumer perspective. Franchise Dealerships didn't want to lose their businesses to unfair competition, communities didn't want to lose the jobs, and customers didn't want to lose the ability to get their vehicles fixed.

...or why Wyoming has such odd exceptions?

If you look at the PDF I linked you'll quickly notice that almost all of the States that allow DtC Sales have odd exceptions and the common theme is protecting EXISTING Franchise Dealerships while creating a path for DtC sales for new Brands or types of Vehicles. Most of these laws were passed between 2014 and 2020 and they exist because of how much demand there was for Tesla's vehicles which are only sold Direct to Consumer. Citizens of a State wanted to buy them and couldn't so they pushed their State Governments into changing the laws.