It leads to things. It opens the door for real deeds to be expected after the words are uttered. If someone is sorry for something then the subsequent expectation is that something be done in an effort to help repair any emotional, spiritual or material harm done. An apology, quite often, is the basis of action. And that is why even though many White politicians, Presidents and Congresspersons have said that slavery was wrong, none have successfully pushed for an official apology to come from the United States government.
Words are powerful.