Amazon makes their own Firestick & Fire box that they would rather have you buy for watching on a tv. Netflix doesn't make it's own equipment (just a streaming service) so it's not the same thing. Amazon controls who has access to their app, Dish could only add it if Amazon makes it available.
If you get one of the Amazon streaming products it has the Dish Anywhere app available so you can watch your Dish recordings wherever it's plugged in (as well as Prime), I have one in a spare room.
I had the Amazon Prime Video app on my other TV with another carrier and we could access it with no problem. DISH does not offer that app on their system. We need the app in order to get a registration code and register our current TV so we can access shows and movies with Amazon. Has nothing to do with other equipment offered by Amazon. It is a free service to Prime members.
Get a Roku device and connect directly to your tv. You can then see Amazon prime shows and Netflix. In addition, it is super fast especially compared against the Dish app for netflix which is very slow.
I subscribe to Amazon prime like others for shopping, free shipping and audio, video streaming. I would also like Dish to add the Amazon Prime A/V streaming app to the Hopper. This should be easy for Dish because it already has an association with Amazon and the Alexa assistant.
Just because Dish has an association with Amazon for the Dish app on Amazon streaming products doesn't mean Amazon wants to put their Prime app on Dish products. Amazon wants you to buy the Amazon firebox or stick (which will be on sale in July on Prime Day).
Dish absolutely needs an app for Amazon Prime. We pay yearly dues for Amazon Prime but can't access our benefits because of Dish. What gives?