Chinese society has been largely open for the last 2 years, yet hospitals have not been overwhelmed, and hardly anyone even knows anyone who's gotten CoVID-19.
The measures that public health authorities in Chinese cities take to squash outbreaks are highly visible. If there's a single known case in a city, the building where the person lives will be locked down, the neighborhood (or even the entire city) will be PCR tested, and everyone who's been near the infected person will be quarantined. These measures work.
The answer to that is that the regime can do anything it wants to, period.
There is no way that China after more than two years, should not have been able to vaccinate those that need the vaccine the most.
Getting COVID is no longer a huge risk and neither is avoiding infections at this point.
No, this is only about control.