I agree it sucks, but you could have bought a Roku or something you knew already supported Amazon Prime in the first place instead of a Chromecast. It's not like there's never been competition in that space; Chromecast is a super-late-comer.
I could have, although I've owned a few Roku boxes and they've all been slow, unresponsive and crash-prone. We actually upgraded from Roku to Chromecast.
Amazon would prefer I buy their Fire TV stick thing, which they would then use as a hook to sell me more Amazon stuff. Given Amazon's attitude towards Apple and Google's streaming devices, chances seem decent to me that if Roku ever increased its market share then Amazon might cut them off.
I'd rather just use another streaming video store.