The solution is to delete nearly as much code as we write. Put differently, the solution is small programs, ruthlessly pursued. The reason we don't do this is that it's totally absent from (nearly all) software culture -- absent as in blank stares and why-you-talk-crazy-talk if you bring it up -- and by far the number one determinant of what people do is what other people do.
There are a few points of light. Chuck Moore and Arthur Whitney come to mind. From everything I've heard, their programs are small enough not to have these problems. And in case anyone is wondering "If this is so much better how come we don't all work that way?" - the answer to that conundrum hit me the other day: sample size. Statistically speaking, it's never been tried.
BC Is that advice you would give to practitioners: to throw out more?
AW Yes, but in business it's hard to do that.
BC Especially when it's working!
AW But I love throwing it all out.
But why do you say they are working in well-defined problem spaces? No more well-defined than most, I would have thought. Certainly Moore was a pioneer of iterative development and evolving a program (and notation) in the direction of the problem. That's why he invented Forth in the first place.
Edit: Oh, having looked up the Medawar reference I realize you probably mean "well-defined problem space" in the way a mathematician would: a problem space narrow enough to be effectively studied but rich enough to produce meaningful results. Certainly most software projects do not start out in such a space. On the other hand, we don't try to learn enough about our problems to find such spaces. We merely add code. One might almost say we excrete it.