So Etsy should be charging GST and every other marketplace app out there. Uber is a broker not a transportation company. Other than their self driving experiments, they don't operate a single car.

No, Uber is not a marketplace. Uber is a consumer product. Uber designs the product and sets prices. Driver's can't compete with each other and I can't 'shop around' on Uber to find a different deal.

If Uber switches to (self driving) cars that Uber owns itself, how does that change the sales tax model? The product is still essentially the same, the consumer still pays Uber, tax shouldn't change here. The backend shouldn't dictate whether sales tax is applicable here.

Etsy is a general marketplace and should handle sales tax/GST just like Amazon does. Which it does.

Of course Uber is a marketplace. A marketplace doesn't need the ability to set prices individually. Abiding to pricing standards are the conditions to offer your services on their particular marketplace. Don't make up rules that don't exist.

but I can't "shop around" on Uber. I don't get a choice of who provides me a service.

The concept of Uber being a marketplace is utterly ridiculous.

Does Etsy tell people which doodads to crochet, then kick them off if they make different ones?