The genre might be about big robots, but it is the human connection that makes us care about the story at the end of the day.

This is actually standard for the genre. Very few mecha shows are really about the robots; the robots are just there to add a bit of spice to the human drama.

Also, if you haven’t seen Gurren Lagann you’re missing out. It’s an all-time favorite of mine and is (in my opinion) a much better show than Evangelion.