Auto Insurance Claims: What do I get, cause inconvenience, unintentional acts

Question
We were in an accident.
The other driver was at fault and never informed his insurance.  We contacted his insurance and it took them two - three weeks to finally admit liability.  And they never even got a hold of their insured.  They finally admited liability because of the police report.

Anyway
They paid to get our car fixed.
They paid for the rental.
We called them and said we are ready to settle.
They said, 'settle what?  We paid for the rental and the repair.'

I was always taught to call and settle.
What do we do?
There were no injuries.  But I thought we had to call and settle.

Is that all there is to it?
We get no money for all our troubles and disruptions in our lives?

Are we entitled to anything else?

Answer
The reason why it took them so long to admit liability is when the insured does not cooperate, the insurer is legally obligated to make documented contact attempts both by phone and by mail and to give the insured ample opportunity to respond. If the insurance company fails to do this, they are guilty of "bad faith" which subjects them to legal action from their insured.

Technically speaking, as their insured did not appear to cooperate with the investigation, the insurer could have actually denied your claim and cancelled the insured's policy. It appears that they felt it was easier to take care of your claim and not risk a law suit from their insured that would cost more to defend than the dollar amount of the claim.  In other words, you got lucky.

The insurance company owes you for the actual damages caused by the insured.  Nothing more.
If your car was repaired and you are not out of pocket for a rental, then you are legally "whole".  If you were not injured, then you were not injured. End of story.  As far as "troubles and disruptions" in your life, that alone is not a financial loss.  After all, this was an accident, not an intentional act.  Life is full of unintentional acts that cause inconvenience and rarely are we compensated for them.  In fact, I don't believe that such a concept even existed or that people would even think of asking for such a thing until recent times. We used to be taught to forgive those who transgressed against us. It's in a book somewhere.
Yes, when businesses make a mistake, they may offer something a little extra to keep a customer, but you are not the customer of the person who hit your car and he only owes you for the actual monetary damages.  It appears that his insurer has paid that.

Go on with your life.