I do think that this was probably the only move that US could have played to bolster their control over its vassals. If Europe was allowed to continue integrating economically with Russia and China, then US would lose political control over it in short order. That said, it does seem like the scheme is already starting to backfire as we see Europeans rebelling against the rapid decline in their economic conditions.

It's very likely that both NATO and EU will end up falling apart as a result of all this. For example, I can easily see countries like Hungary and Slovakia flipping over to BRICS. Once a precedent is set, then more countries could follow. It's becoming clear that the dominant view in Italy, France, and Germany is that people do not want to restart a cold war with Russia. It's highly likely that nationalist governments will get in power that will try to restart economic integration with the east once more. While relations with Russia will likely stay tense for the foreseeable future, trade is likely to increase despite that. And of course, the problems between Europe and China are far less severe which will allow China to play as a mediator.