It won't, most people game on PlayStation or PC, with a dedicated group on Switch too. They want hardware...streaming is a different experience that has to compete with mobile gaming and if Apple and Google see that it effects their revenue on their phones, they will block them (except for Googles own Stadia and that is a disaster)
So it's not really going to work. Easy.
There's a tenuous relationship between Google and Amazon for stuff like this. For example, the official YouTube apps were removed from Amazon's devices for several years. Fire TV only got YouTube back a few months ago, and their tablets still don't have them.
Now that Amazon has announced their own Luna service, the likelihood of PS Now, Stadia, or Xcloud appearing on Fire TV seems a lot lower. Even if those services
do appear on Fire TV, you never know if there might be some behind-the-scenes shenanigans to ensure that Luna offers better performance than the others.
The other issue is that some of these services might start cutting exclusive deals with certain publishers. You might have to subscribe to one service to get Activision games, and a different service if you want Capcom games, and yet another service for Konami games.
I see that Ubisoft is supposed to have a "channel" on Luna, which is reminiscent of their announcement to have Uplay+ available through Stadia for an additional fee (not included with Stadia Pro). Will the Ubisoft channel on Luna be included in the base price, or will you be required to pay another subscription fee (like on Stadia)?
There's just so much uncertainty surrounding these services now. It's exciting in some ways, and simultaneously troubling in others.