The protest itself is not effective, or at least doesn't change the current day order. But it signals an important opposition to a certain rule that a smart politician should pick up.

> The first mistake is failing to recognize that many governments (case in point) are not nearly as vulnerable to bad PR, so generating a bunch of sympathetic imagery (photos of student protestors getting gassed or whatever) might not actually be useful in swaying political outcomes.

You are wrong. China does care a lot for its image. More than you'd expect. China does give a bunch of money to improve its image (https://en.wikipedia.org/wiki/Chinese_foreign_aid); certainly less than the US but it is sizable and also smarter. They are building popular stuff (like hospitals) in the middle of nowhere and making lots of fanfare about it as well as putting their flags. And no, these are not loans, these are grants (ie: free money!).

The coronavirus and current US-led media campaign did damage the Chinese reputation a lot. But here is where you might be lost: China doesn't really care about the educated western population and the western population in general.

> The second mistake is assuming that most (putatively) peaceful protests in the western world are actually the impetus for political change, and not just part of a legitimization strategy for political changes that were already in development before the protest started.

It's a process. Protests are a manifestation of discontent, and are a good indicator when no transparent voting mechanism is in place. It gives the US good leverage against China by weighing discontent. Sure, it makes no changes, but that's because we live in a distorted world where democracy for small countries is possible.

Democratically, independent and small countries like New Zealand are only possible today because of the world order the US has placed. Otherwise, there is nothing stopping China from walking to New Zealand and declaring it New China.