I would say that at the hospital he wasn't at his best mental state and he also knew that if anyone was left alive that knew about Ellie she was going to be hunt. And sure after all the kill he done in the past he wouldn't have issue killing a few more.
Anyway even criminals have loved ones and can act kind. And he being able to sympatize and have real care and love eliminates him being a sociopath.
I'm not saying Joel definitely is a sociopath, but I want to correct you on something. Joel at no point sympathizes with Ellie. Ellie made the decision to finish the job and Joel took that from her. That is the opposite of sympathy and empathy. To empathize and sympathize is to feel what someone is feeling. By making the decision for her against her own wishes, he demonstrates a clear lack of empathy. Saying thatvthat Joel acts out of love overlooks the fact that sociopaths do in fact care for things, but the things they possess. When a sociopath is sad that a friend or pet dies, they aren't sad because that person will never experience life again, nor feel for those that are also hurt. They are sad because they lost their possession.
Id even suggest this lack of empathy is further evidenced in the scene where Joel gives bill his partners suicide note. I think that while some might say it was the right thing to do, it can't be ignored that the letter was a devastating blow that didn't necessarily need to be spelled out.