[btilly]

Shouldn't one at least start by giving tough punishments to officials i.e. years in jail etc, before reaching for the more monstrous punishments?

Yes, and it has been. It didn't work.

See https://en.wikipedia.org/wiki/Capital_offences_in_China for a list of existing crimes that result in capital punishment in China. This coverup is a very good fit for #14, endangering the public safety.