Rozier has no trade value (only a second rounder)
Put yourself in another team's position. Even if they want him because they believe in him, why would they bid up Rozier against themselves? They won't, so no team makes any bids, therefore keeping his price at a second round pick.
If the Celtics make an effort to trade him, other teams perceive the Celtics as unwilling to pay their own player. This prompts doubt to creep into their minds. What is wrong with him that they won't consider paying him, or they think he is going to get paid more than they value him, which makes them doubt that they should pay for him.
The feedback from the Celtics' interest to trade him ruins Rozier's trade value. So all of these trade ideas will fail immediately. And this should be a good thing for the Celtics. As they did with Smart, they have pushed his value so low during the season that other teams lose interest in overpaying by letting doubt creep in the door. The Celtics really don't have any doubts over what Rozier is worth to them, so they cut the legs out to stack their deck for negotiating.
The reason why I believe that the specific role that Rozier is being suppressed artificially by the team is because his role is not his ideal role. Off the bench, he spends a decent amount of time playing off the ball and not in his natural position with the ball in his hands. (Now, the Celtics have plenty of reasons to justify why they've boxed up his role that deflects away from my hunch with plausible deniability. And that is fine with me, but it doesn't make me shy away from the actual outcomes).
Some players naturally succeed with the balls directly in their hands, and I think his two-man game with Horford also really helps his game. And we have seen him turn the 'corner' with good games when he is in the starting lineup when Irving takes a break. So I don't think he is worthless as a suggested in the beginning. But relatively, as the restricted free agency approaches, his value is squat.
This is the silver lining and we shouldn't panic over his struggles by trading him. Just remember the simple and elegant principle of "buy low, sell high". We don't want to sell Rozier now because he is low.