Public apologies are great because you look like a good guy and you get to clear the air. You have to use them sparingly though. If you're doing a public apology every other day, then it just shows everyone that you're either fucking up a lot, or you're just looking for attention. It helps if you were very vocal about your hate for something before you publicly apologize. Otherwise the public apology is more like a public diss masked as an apology. "I want to publicly apologize for cheating on my wife." / "Honey, you were cheating on me?" / "Oops."
I don't recall Kanye ever publicly dissing Bruno Mars, but it could have happened. If not, then this must have come as a surprise to Bruno Mars. I hope he wrote this while he and Bruno were chilling for the first time. Bruno checked his mentions and went, "what the hell? Kanye?"