Protecting egos is part of managing an NBA team.
I think we underestimate the challenge a coach faces in moving veteran players, still playing at a high level for an undrafted player still on his rookie contract. That too, an interim coach on his first HC gig, for a franchise that's been a joke for over a decade and a half. Most of these players have been alphas their whole life. That belief in themselves is partly the reason they are playing in the NBA. Plus, it's not as if their performance fell off a cliff. They are both healthy, and playing at a high level. If the pieces don't fit, that's on the GM. It's easy to say that the coach should put the team on the floor that has the best chance of winning, but that's not possible with managing players and their egos.
Lastly, I don't want to throw DDR/Lavine/Monk under the bus. I have no idea if they ever gave any indications to Doug that they would be unhappy if Ellis was promoted over them. It would be a pretty natural reaction though, and not an easy decision for any coach, let alone a rookie.