seems to me that, if this makes any sense, the interesting question is: why can't you have both? given that selection for "great art" is over a large number of people, why can't you find someone that is gifted in both areas? perhaps one somehow counteracts the other (for example, you are praised for "mechanical skills" and so never learn "abstract thinking")? or perhaps the market values the combination of "poor mech…
Afraid I don't know enough about programmers or painters to spout names, but in any other artistic medium you've got a mix of all types. I'll use film as my example because film's a medium in which you have a hundred people working together, and very elaborate roles evolved to let people do exactly what they want to do.
Some directors function as merely directors. They decide what they like, and they have other people execute. But other directors can and do insist on controlling other parts of the creative process. I'm not a fan of James Cameron, but the guy writes, directs, and edits his movies, and he's very involved in set design as well. Some props he insists on making himself because he doesn't trust anybody else to do it right. So there's a guy who knows what he wants to do, and is also capable of the incredible technical feats required to pull it off.