The first part is true-isch. If a player could be MORE effective if using their size they should. I played soccer which is not nearly as physical a sport. Im 6'6/230 lbs and if i didn't use that to push people of balls etc i got yelled at by teammates and coaches. It's really a basic sports thing, use all your assets.
And the three players you mention are clearly effective, whilst Mantha isn't really. And Thornton did throw his weight around AND made plays. And Marchand DOES use a lot of finesse in his game. Don't know enough about Wheeler to say anything.
If Mantha were in a development league, or even still in a developmental part of his NHL career, I could totally agree with your first point. And if I were a coach in charge of trying to develop Mantha, I would try to get him to maximize the use of his size. But we're not coaches in charge of his development, and Mantha isn't in a developmental portion of his career at this point. He's 28, has nearly 400 games of NHL experience, and has been playing pro hockey for a full decade at this point. He likely is what he is as a player at this point.
Accepting that he's unlikely to completely change the way he plays the game, the point of the coaching and management staff on the team is to decide how best to utilize him as a player (and eventually if they should retain him and at what cost). Their goal is team-oriented, not oriented towards Mantha's development. Even with the perceived flaw in his game, Mantha is still a useful player. He is definitely effective, to the tune of being 0.57 point/game player since he arrived in Washington. His 1.91 5v5 points/60 since he arrived in Washington is wedged right between Connor Sheary (1.93) and Tom Wilson (1.89) during the same span, and is ahead of Backstrom, Oshie, and Strome. He's very much in line with being an effective secondary offensive threat at 5v5.
Is he as good as Joe Thornton, Blake Wheeler, or Brad Marchand? Of course not, the point was (as I mentioned) to use extreme examples to illustrate the concept. Mantha is who is he as a player, and that player is a useful 2nd line player.