This is really a question for Adobe rather than the community, but my understanding is that the AEM as a Cloud Service is functionally very similar to the latest 6.5 release of AEM. So it's not as if there's a 6.6 version that is only available in the Cloud Service paradigm and all of the AMS or on premises customers won't get the latest and greatest functionality until they migrate.
AEM as a Cloud Service does have some beneficial differences from the current AEM paradigm--but mostly on scalability and automated deployment of patching. In other words, the differences and benefits are mostly on the back-end technical side rather than use facing.
There may be an eventual world where AEM on premises customers are forced to migrate in order to get new patches and functionality, but I'd suspect that's at least 2 years out if it ever happens.
It is absolutely possible to have your AEM Assets instance hosted on a private cloud, on-premise, or at AWS. The version you'd be deploying on this would not be the "AEM as a Cloud Service" version, but would be the latest version of self-hosted AEM which at this time is AEM 6.5.4.
There is one piece of functionality in particular though which you should be aware of in running AEM Assets though, which is the AEM Remote Assets connectivity, whereby you have an AEM Sites installation which can remotely connect to a separate AEM Assets infrastructure, so that you can keep these two separate. It's a powerful way to use Assets, but can also sway where you deploy assets depending on where your AEM Sites install is kept.