Sotah 14a expands this with the statement that just as HaShem visits the sick (Bereishis 18:1), so should you, based on this mitzvah (this time based on Devarim 13:5). It's not just to emulate His middos, but His actions as well.
This leads to contradictions, though. For instance, HaShem kills those deserving of death who can't be prosecuted in court (see, for instance, Rashi to Shemos 32:35). Does this mean that if someone's guilty bidei shamayim we can kill him ourselves? Of course not. Only a Rodef, a Mored b'Malchus, and one sentenced to death by Beis Din are able to be killed. What happened to mah hu af atah?
"I wage wars," HaShem declares, as the passuk says (Shemos 15:3), "HaShem is a Man of war" (Avodah Zara 2b). Should we try to fight everyone? No. HaShem told us to seek out peace from whomever we can in most situations.
Obviously there is a line here. But how do we know where to draw the line?