I will be the dissenting voice here. Mauer was mentioned, but no one mentioned how he stopped catching years ago due to Concussions(non height related), bi-lateral leg weakness(??), and knees(possible size issue).
I think once you get over 6'3" you better make sure that you have a secondary position, and can hit the ball. It's hard enough on the knees when you are 6'0", 195 lbs. Can't imagine getting up and down when you are 6'5", 235, thousands(ten thousands?) of times per year.
While you might have a cannon of an arm, it has to take longer for a tall person to get his feet and arm in throwing position after bending down to dig a throw out of the dirt.
I have nowhere near the experience in Baseball that Coach A has, so take my thoughts with a grain of salt. I'm old, back when 6'1" was considered a good size- I was switched over to pitching from catching at 16. Even then, I remember how bad my knees felt from July on. I do know that pitching coaches LOVE any kid 6'4" and over.
Apropos of nothing, we have this wonderful local catcher who will be playing for TCU this spring. He says he's 5'8", but as my height challenged elder son said, "Dad, he's 5'6"!" Kid is a freak though. Switch hitter with power, fast, and a great arm.
Maybe the lesson is that don't let your size hinder you.
One other thing. Catchers like Bench, Parrish and Carter used their size in collisions at home, but those collisions don't happen any more, at any level. I used to love them, but I was a hockey player when I wasn't playing ball, so it seemed pretty old hat, and kind of tame, to me.