It doesn't need to be perfect. Depending on the specific intervention in question, you only need to exceed some critical threshold of compliance to get R_t below 1.0.
i'm not sure which example makes you think things could have been different.
With BA.5 the unmitigated R is probably north of 10 and China had to throw in the towel, because reducing transmission 90+% is much harder.
We have absolutely no idea what happened in china. We know they hid things in the beginning, and in the end ( when they stopped counting infections after opening the fates to omicron). What makes you think they told the truth in the middle ?
We got the footage and reports of hospitals and mortuaries overwhelmed when it ran rampant at the end, but in the middle we just got complaints about how much the isolation policies sucked.
Why did the propaganda masters hide all the death in the middle but not at the end? Why did it look like a disease spreading through a mostly-naive population in the end, rather than a wave-N population like everywhere else?
Doubt was a reasonable position in the middle, from the outside, but after how it ended it looks pretty clear there was very little in the way of COVID in China for two years.
In China's case, it means that simultaneously a bunch of people would be welded into their apartments, but that the government would also cover up and ignore high-enough level officials who disregarded orders, or criticism that they were ignoring important vectors. China is very corrupt: whatever they announced they were doing publicly wasn't done remotely effectively - it was PR for how tough and untouchable the government is.