I get what you’re going for but I’ve found that attitude in other people distasteful. First it’s a normal emotion and simply refusing to experience an emotion probably isn’t healthy. It also means you are never really sorry even if you might say it. How can you truly be sorry for something without regretting having done it? It ends up translating to “I’m sorry for the outcome and that it hurt you but if I had to do it all over again I would still do it knowing that it hurt you” and that isn’t really an apology.

A regret is a mistake that you don’t want to make in the future only it’s projected into the past. “I regret having done that because if I went back to the past, knowing what I know now, I wouldn’t have done that”

You’re also inviting other people not to regret their choices even when those decisions negatively affect you.