RTS Style movement without rigidbody?

I have human characters moving around with standard RTS left/right clicks. I have a navmesh agent on the object as well as a capsule collider. Movement/rotation is handled through scripts between the navmesh and animator controller. I originally had a rigidbody on the object as well but have since removed it and have noticed no difference in movement. If the navmesh and scripts are handling all movement do I really need a rigidbody?
Also, I've been trying to get the character to take a slight step up moving off of a street an onto a sidewalk but can't seem to get it to work (without a script making the character move up). Big thanks for any advice/help anyone can offer.

*Update, I realize that I need a rigidbody to collide with other objects but my character continue to walk through the sidewalk or simply walks into it and continues walking without moving (depending on the settings).

 

If the sidewalk has a navmesh (is navigation static), it should make whatever's walking on it move up.

Also, yes, you don't need rigidbodies if you're moving with NavMeshAgents. If you need hit detection, you can use trigger hitboxes.