I agree with everything except that. Kobe played hard every night, he has no idea what it's like to not go hard. Melo was mailing half that season in. He wasn't even pretending to try on defense at all despite being in his athletic prime and his effort level was inconsistent. He'd play hard some nights, but other nights it looked like he was more concerned with his dinner plans than the game.
If you're going to go public with your trade demand, I think Kobe handled it the best possible way. Didn't talk about it once the season started, played his ass off, gave the team a chance to improve the roster around him, and most importantly, he kept his word. They got him help, he got the franchise titles. That vindicates much of what Kobe did imo.