I think that everyone agrees that measuring a young pitcher's velo is not going to hurt them. But rather the series of events that may follow.
When son was younger the only competition in youth baseball was between teams, now it is player against player and the "how does my player measure up" mode of thinking. Perfect example, though no harm intended, was the question asked that began this topic.
Parents panic when they think that their son may be developmentally behind in sports (yes we have had this discussion) that includes their velocity, in fact they panic more these days about that than if they are behind in the classroom (JMO). There is a HUGE need these days for their player to be better than anyone else's player and brag about it. More of everything seems to be the way to go. That's how it is today in youth sports. I think the use of the radar gun early causes this. Parent points out to player that so and so is pitching harder when they first learn of the velo or one player throws hard in showcases, and others try to throw harder to be better or gain attention etc, etc. Then before you know it a parent puts together a program to increase their velocity, filming, charting, lifting weights, more mound work, farther long toss than the player can handle.
That's why IMO, radar guns are dangerous.
BTW, I beleive that a toss program as well as a conditioning, strengthening program should be tailored for the individual, that's why advice on some things on a message board is not always appropriate (as in the case as the advice GBM has given out what he thinks is a good plan may not be good for others).
And of course the workload has lots to do with it. If GBM really knew what they did in proball, he would find out that a pitcher's bull pen depends on how much time he put in his last outing. If it's short, it's a longer pen, if it was long, it might be a light shorter pen. Some relievers go tot he mound, others on flat ground, there are no rules and everything is flexible depending on the individual.
But again, you are talking about what grown men do not children.
BTW, my son's friend blew out his pitching arm at 15 when younger he pitched at one of those fanfest set ups, no proper warmup, they don't tell you that before you throw the ball.