I remember these words of wisdom..."there's only so many bullets in the holster". Since your son has seen such good progress with a pitching coach, have you considered that he may have the same or better success with a hitting coach? He's average now (as are most 14 yr olds)...a few hitting lessons could take him to above...or exceptional...or...? And, there's not quite the risk of overuse/injury/pressure. And, playing multiple positions, developing as a hitter...provides more options in recruiting down the road. As far as fielding positions, if he's pitching, then going to 3rd, he may be throwing hard pretty frequently to attempt that out at 1st. Another fielding position would help "reserve some of the bullets".
Unless he's extremely efficient, I wouldn't consider pitcher only during the 14-17/18 time frame...too many variables come into play...most importantly injury & overuse...and physical/mental development/strength/other skill sets...Also, pitching only can cause stress on other areas...like shoulder, hips, lower spine. Agree with Go44dad on training techniques!
When considering pitch counts, it's important to include warm ups, too. See ASMI.org for current counts by age, by State...a must education!