As far as I can see, CBS wants his bigs to be able to do these things: 1) Mobility to defend the perimeter 2) Passing 3) Pick-game 4) Shooting Outside 5) Toughness to defend the paint 6) Rebounding 7) Post-up scoring.
That's also in the order it seems like CBS prioritizes it.
From how I see it, most of the things Monroe does well are the things CBS values the least in a big. However, there is one skill that is legit: passing.
Monroe legitimately has some of the best passing instincts in the NBA for a big man. The stats do not back this up because he has played for the Pistons, next to Drummond, which closed down offensive passing lanes. For the Bucks, he was assigned to the bench, to play with bench players in an ISO-heavy offense that lacks movement.
Monroe's passing ability is similar to Horford's, but the problem is that, because Monroe can't shoot, bigs can ice ball-handlers on the pick and roll with no fear that Monroe will pop for a 17 footer, or for a 3. This would also close down driving lanes for Kyrie, Smart, Rozier, Brown, and Tatum.
What I do like is that he would fit into our culture of moving the ball and making the right passes. It also wouldn't be too hard to get him touches on the block, because we are doing those actions more this year in our offense.
Monroe's rebounding solves a problem we really don't have anymore. He has always had a bad habit of peeling off the ball-handler driving into the lane too soon so that he can try to get a rebound. He is also late on rotations. These things give him good rebounding numbers, but below average defensive field goal percentage at the rim (above 52%).
His poor foot speed and lack of effort also puts him in the 24% of all big men in defending the pick-and-roll. For reference, last year, Al and Baynes were above 50% and Kelly and Amir above 78%.
Considering that we have Baynes, who can protect the rim, set picks, pass (a little), and stretch the floor out to 18 feet (corner 3s are coming soon!), Theis who can defend the perimeter and paint, set picks, pass, and stretch the floor out to the 3 point line, and Morris, who can can defend the perimeter, set picks, pass, and stretch the floor out to the 3 point line, I don't see Monroe as a necessary cog or a cog that fits our system.
With how we are rebounding, even Tatum and Brown fit at the 4 next to one of those bigs better than Monroe would.
Even if there was an injury, because this is largely a developmental season, I would love to run with Yabusele and Smart out on the court at the same time. Yabusele would do some of the offensive stuff that you look for, and Smart would yell at Yabusele until he started figuring out rotations. Our defense would be awful for a while, but Yabadabadoo would be just as good if not better than Monroe at defending the pick-and-rolls.