Being sorry should be a function of remorse, not fear.  If you are sorry, say so.  If you are afraid, run.

do we not say sorry because we are afraid of the consequences of not having remorse?

I don't.  If you are not fearful, then sorry probably is not needed.  Let things go and see what happens:)

Remorse should always be expressed. Not doing so could chew you up inside. Worst case is they do not accept the apology. If you do not offer it then it can never be accepted. Both have the same result on the relationship, but the former gives everyone the chance to heal.

do we not say sorry because we are afraid of the consequences of not having remorse?

No, i say sorry because i am sorry for having said or done something that hurt another. Not because i am afraid if i don't say it there would be other consequences.  If i am not sorry then there is no point in an insincere apology.

If i am not sorry then there is no point in an insincere apology.

I would agree with you there, Kitt.  An insincere apology benefits neither party.  You might as well be a politician.