I've felt better when people have apologized to me, and I've felt better when I apologize to others. When someone has been wronged, it's better to clear the air, acknowledge what happened and move on with a repaired or even improved relationship. The alternative is... what? Just pretending it didn't happen? Has a tendency to just make bad feelings and false assumptions fester with a lot of people.

>> you’re sorry, and you did it? that makes no sense

You did it, and it was the result of a miscommunication, or your feelings have changed, or you didn't realize what the consequences would be. What you're saying is that you recognize what happened, you empathize, and you're willing to change some things to do better. If the other person doesn't hear this, it can take a long time for them to notice that you're doing better, harming the relationship.

edit: don't think of it as feigning regret, think of it as a chance to properly communicate something that has been miscommunicated.