Counter-propaganda runs the risk of putting protest front of mind in the people because you're talking about a protest. It requires constant work to keep it up. And it can engender suspicion more than censorship. In a situation where people are already indoctrinated like in the US, you have to do counter-propaganda, reeducation, or cultural revolution to clear certain things up. But it's a lot easier to not need to do that in the first place, and that's what censorship can sometimes accomplish.

Like Covid, if enough people take the bait and a meme begins to spread, censorship can stop working. In this case counter-propaganda can become the preferred strategy. Something similar happened in China where Covid became so contagious that zero-Covid became too expensive or difficult to keep up. Containment was breached such that it became untenable. In the case of Covid the result was about a million deaths in China. In a lot of cases, these are not small consequences. Moving on from censorship is likely seen as too risky with not enough upside, although this is only my speculation.