CaCO3Girl, as you know, I am in your neck of the woods, North Metro Atlanta. In terms of HS, I really think it depends on the school and depth of talent there. For my son, a pitcher in college, he was a 2 way guy all the way through HS. Played 2nd or 3rd and pitched through his junior year (didn't play SS because we had a D1 commit there who has since been drafted) and played 2nd & SS his senior year (he was dealing with a nagging elbow issue his senior year so didn't pitch much and when it bothered him too much he asked to play 2nd). He played at a 6A school with a population of about 1950. But the fact of the matter was, they didn't have anyone better than him to play those positions. At some schools, there are more options. If a guy is a REALLY good pitcher and they have other REALLY good position players, the pitcher will be a PO. But, if that really good pitcher is also a REALLY good fielder and hitter, they will be a two way guy in HS.
For summer teams, my son played 2 way as long as he could. When he was 15, summer after freshman year, he was a starting pitcher and starting SS. When he was 16, they started easing him out of SS because his hitting was not as good as other options. He was a better SS than anyone they had, but they wanted hitters. Plus, they realized his future would be as a pitcher. At 17, he started the summer on a new team and was playing SS and pitching. He was soon weaned to a PO. He really liked playing the field, but his passion was pitching and knew that's where his future would be, so he was fine with it.
So, baseball basically told him when it was time to move on. Playing 2 way lasted quite a while, because he was such a good, athletic fielder, but he had always focused more on pitching than hitting, so the time came.
It's not a given that a guy switches to one or the other. Basically what happens is, especially around Atlanta, there are so many options that kids start to fall into a category. There is not that big of a drop off between options, so pitchers wind up becoming POs. But, believe me, if a pitcher really is much better than the other options in the field, he will be a 2 way guy, even around here.