The narrative that America wants to democratize the world only really exists in places like Russia, Middle East, some of leftist Europe. But really, if you think about it just a little bit, there is nothing in it for us. A democratic China would be even more difficult for the US to deal with, given that the politicians would be subject to populist whims. It might be good for China as it creates some additional pressure valves, but we don't care about that, we are pretty happy to let China plod along wherever its going (just please stop pushing up housing prices on the west coast).
There aren't any huge ideological battles going on these days, the cold war is over, and the big baddies for us to face are failed states and terrorism, both of which would thrive in a more unstable China. Heck, our worst nightmare is Russia imploding. I bet they lift up on sanctions soon just because of that.
Of course USA govt. has a strong interest to `democratize` the world: a world with same ideology would greatly reduce the risk of unknown/uncontrollable frictions and the cost of communication. just think how many think tanks, scholars have nice payrolls, and ultimately it's the USA govt. who pays.
Operations like spying, funding social unrested in other countries are not necessarily under the mission of regime change. they are more like insurance. take China for example, what if its economy suddenly sinked and President Xi had no choice but to start a war against Japan/Taiwan/...? In these nightmare scenarios, groups of unrest with strong connections to USA govt. would become handy, if not crucial. I bet every major powers have hundreds of nightmare scenarios, and each of them has various `assets` requirements presented to the congress/presidents/chairmen, with a dotted bottom line: "hope for the best and prepare for the worst."
This hasn't born out in practice. Elections do not garauntee stability, at least before a certain point in the development spectrum. If China democratizes on its own, great, but meddling by us won't lead to a good outcome.
I'm not sure how making a destabilized China even less stable would improve the situation, nor do I think this insane theory is a part of the USA's security doctrine. The USA's biggest form of security is its huge unmatchable military, if things get bad with an established country, they just blow things up for awhile. The danger is if that country falls apart into a bunch of factions that cannot be targeted via conventional warfare.
Put this way: gulf war 1, Iraq invaded Kuwait, we easily take them out. But we don't dismantle their government because...that would make the problem much worse and our military much less effective (good at taking out countries, not so much in taking out terrorists, Isis, etc...). Gulf war 2: the son is not as smart as the father, goes too far, screws us for a decade+ in an unwinnable war. Sadam Hussein as an intact power was much easier to deal with than the vacuum that now exists.
So if something bad happens with China, there will probably be a good gulf-war-1 style spanking involved, but not with the goal to destroy China, depose its government, and make the situation much much worse. No one in the USA gov hated Gaddaffi enough to want him out at the cost of a destabilized Lybia (it was the lybians themselves who wanted him out).
The enemy you know (and can easily bomb) is much better than the enemy you don't know.
There aren't any huge ideological battles going on these days, the cold war is over, and the big baddies for us to face are failed states and terrorism, both of which would thrive in a more unstable China. Heck, our worst nightmare is Russia imploding. I bet they lift up on sanctions soon just because of that.