It's probably closer than you think. I don't think most superstar players think much about young talent or draft assets unless those guys can become immediate contributors or flipped for other impact talent. Miami has Dragic and Whiteside as their core guys, which isn't that dissimilar from IT/Horford. Stevens is a great coach with whom Hayward has a relationship, but Spoelstra is a damn fine coach as well and Riley still has major cache as a pitch man. And while they weren't the no. 1 seed in the East, the Heat were as good as anybody over the second half of the season and given the organization's history, I think many would buy into that improvement being real.
This dramatically understates the difference in the 2 teams. I'll grant you coaching and front office as a wash. All of Ainge, Riley, Spoelstra, and Stevens are really good at what they do. Riley is a living legend. Stevens has a personal connection. Either could be a difference maker, but at the end of the day, I don't see huge separation in coaching/GM quality.
But, the Heat are coming off being a lottery team. The Celtics are coming off being the 1 seed and a conference finalist. It's silly to just compare Dragic and Whiteside to IT and Horford because the rest of the rosters exist and matter and Crowder, Bradley, and Smart are all good NBA players and a significant part of why the Celtics are a really good basketball team. The only way they don't count is if the Celtics are also adding George, which once again illustrates why the team quality comparison isn't actually close. (Johnson is coming off a very strong season and deserves a mention as quality depth for the Heat, although he's also a FA. Waiters is probably the next option and he remains a pretty mediocre NBA player.)
Dragic is not close to the player that IT is. Even if you throw out last year entirely for IT, Dragic still isn't close to as good as he is. Thomas is a much better shooter, a better passer, he turns the ball over less, and he does all of that with a much, much higher usage. Dragic is closer in quality to Smart than he is to IT. Pick any statistical measure, and even accounting for IT being a horrifically bad defender, they are not close. They also aren't close in terms of reputation.
Whiteside v. Horford is a closer call. Horford has a much longer track record of being a high quality and reliable player, but Whiteside improved significantly last year overall, and there's a case that he's just as good as or slightly better than Horford right now. RPM, for example, likes him a bit more. WS likes him a fair bit more. BPM/VORP think he's a lot worse. Overall, I think you'd fairly consider this a wash.
Adding all that up and what were left with is a Celtics team with better top end talent, better depth, and similar coaching. The team's respective performances a year ago bear this out. The Celtics are, quite simply, a much better basketball team. It is possible that Riley has a complicated vision that he can sell of how he can turn his team into a contender, but it's hard to see what it is. If I were ranking the Hayward frontrunners in terms of team quality (ignoring future assets and guys who have yet to play in the NBA), it goes, Boston > Utah with Hill > Utah without Hill > Miami. If you count future assets, the ordering stays the same but their is a gulf instead of a gap between Boston and Utah/Miami.
Hayward may sign in Miami. He's obviously considering it seriously. But, if he does, he's going to be competing for home court in the first round, not a Finals appearance or a championship.