It can’t be free because it costs too much. You need data centers near customers for acceptable latency. You also need a computer to connect to your amazon PC.
No your phone won’t work. To prove this. Get a really expensive phone that you can a keyboard and display to. This is already a thing right. Run a remote desktop software on your actual PC wired vastly preferred. Now go next door and ensure you have acceptable wifi. Try this out and tell me how it works for you.
Now imagine it with average wifi which is often terrible in my households with the shitty phones people have creating an experience that is orders of magnitude best case scenario we have created above.