I finally got an eviction order on one of my tenants this week. That CDC order is only for non payment of rent. You can get an eviction for breaking ant other part of the lease.
My in-laws recently evicted someone for having a dog breed banned in the lease. Just to back up your last sentence. I think the tenants were deadbeats as well, but they did not bring that up in the eviction proceedings.
You can get a 60day order if 1 months rent is given as compensation in CA.