I think it's better to just thank them in a form of sorry. Like if you are late. Don't say sorry I'm late. Say I appreciate you waiting for me. Or thanks. And if it's an argument find a way to concede that you appreciate their opinion but have your own. I don't know it's hard to do. And every person reacts differently to a sorry.
As long as people mean what they say I think it's good. I sometimes say sorry if I'm late, but only if I really am sorry.
I like your version as well. Changing the conversation from apologetic to appreciative.