It's not like that scenario does not worry me either, sure. From a purely "fight the disease, nothing else matters" standpoint, yes, more installs mean better coverage and would make digital contact tracing work more efficiently. I haven't heard of any western government considering such a reductionist approach though, that would not be a proportional response and honestly a bit bizarre. Even in such a case the proposal by Google/Apple would be beneficial since it limits the usefulness of this data for other purposes, being designed with privacy in mind and far less intrusive than other tracking methods we could draw up.

I would still maintain that this nightmare scenario is a problem with any particular government that would implement and misuse such measures, not with an anonymization effort for the BTLE stack. We absolutely should push back against the former and insist on what's missing for a full system to be implemented in a sensible manner without infringing on basic human rights, that's a worthy hill to die on, this particular aspect is not.