I totally think it depends on the kid...I never pushed my DDs at anything but when they were quite young, we moved from So Cal to E. TX and because of the huge difference in cost of living I was able to stay home with them and sign them up for lots of activities. I thought they could just try everything out and see what they liked and we would go from there. They liked everything lol!!!
They took Karate, Tennis, TBall/Softball, Soccer, Dance (Ballet/Tap/Jazz), Swimming and Gymnastics (plus space camp, drama and science camps in the summers). They would be changing from dance outfits into softball/soccer outfits in the car while eating PB&J sandwiches as I drove them from one activity to another.
Once they were in regular school, the academics were really easy for them even in the gt program and after grade skipping/early entry so they didn't have to worry about finding much time to study or do homework. It was crazy and hectic but they both really thrived during this period. They weren't the best in the group at every activity but they held their own and they still stayed on top academically with straight A's.
When we moved again years later, we had to cut out most activities for financial reasons giving them more free time. Their temperaments have always been very different and they responded very differently to the change. One DD was always very sociable, she did just fine with the transition, using the free time to do things with friends. The other DD who was never too sociable to begin with just started to wilt.
I am looking back with new perspective now. My more sociable DD I think is what you consider "optimally gifted" while my other DD is either HG or PG (and possibly 2E). HGDD's grades went down after we moved so I took away the one extracurricular activity she had left and that just made things worse. I didn't realize it at the time but in hind sight I believe that being so busy with extracurricular activities helped her tolerate not being terribly challenged academically. I think she used school as her time to relax but once the other activities ceased, she became somewhat despondent.
"In particular they lost the ability to use their initiative, to take calculated risks and they didn't develop leadership skills or normal social skills."
I don't believe the crazy schedule caused one of my dds to lose abilities or fail to develop skills while not affecting the other dd at all in this regard. I do think the DD without the natural social tendencies thrived more in an environment of over-scheduling though. Not scientific, just anecdotal.