It is definitely hard not to look at the Nuggets and compare them to the Celtics. The main difference is obvious, they have Jokic and he was healthy (as opposed to Giannis and Embiid). He is a dominant player and takes so much pressure off all of the other players. So much talk of how the game has changed but size does still matter.
I also think that Murray is a really good complementary player. Handles the ball well, can shoot, has high level talent, exactly what you want opposite Jokic. The rest of the team is nothing special but it is well balanced. And you can see that there is understanding and acceptance of their roles.
As to the coach, I don't know how much that matters. It is hard to tell just watching if the coaching was good or not. The results were good, so you assume the coaching was good. Certainly there has been continuity (Malone has been in Denver 8 seasons), something the Celtics have not had.
There is not one formula for a title team. GSW won with their top players being wings and guards. I do think that is more the exception though. More of the better teams have a big as one of their top players. In any case, the Celtics roster is not well balanced. The talent (and contracts) leans heavily to guards and wings. That does not mean that I think Tatum and Brown together are a problem, just that roster balance a weakness.
The impact of the lack of coaching continuity is harder to decipher but title teams tend to grow into that, both coaches and players. I believe it takes more than one season to fully adopt offensive and defensive schemes. It also tends to take a couple of iteration of bringing in role players to get just the right combination.
Hopefully we will have some level of coaching continuity going forward. We are bringing in a bunch of new assistants so that is a step back of sorts but we need to build on what we can. And I expect some roster changes around the edges to bolter the PF and C positions, but not major roster changes (such as trading Brown). I don't expect a trade of Brown but I think it is possible.