This wouldn't change anything. If the underlying license for a piece of content linked to your movies anywhere account expired, it would be removed from movies anywhere as well as the original service you bought it from. There's a possibility that maybe because it's an edge case it might end up still in the library of a synced service but that would be more of an unintended coincidence.
Movies Anywhere is hardly a 3rd party though. It's wholly owned by Disney and I suspect it will only last as long as it meshes with their streaming strategy.
Maybe something like "The Pirate Bay" instead of dealing with a fragmented market that's just as bad as 90s cable?