Is this because conservatives lack empathy, or revel in cruelty?

Both. The answer is both. They literally lack the brain structures to feel empathy

It's a bit more sinister than that. They're saying "It's your fault we have to do this, so you're the ones that should suffer the consequences. Honestly, you're lucky we're not throwing all of you perfidious leftists in these cages."

These are not "conservatives" and it's dangerous calling them that because it makes them sound less dangerous than they are. They literally want to murder people. They are fascists.