As a cheap programmer, I disagree. An expert may spend 90% of his time doing something he feels is drudgery, but he does it properly, so as to prevent the 10% all-hands-on-deck emergencies from occurring.
If you hire cheap programmers to handle the 90% under the expert's supervision, the expert still has to painstakingly review the work so as to ensure it was done in a way that at least sort of resembles the method the expert himself would have used. And having reviewed other people's code, I am of the opinion that process is sometimes soul-crushing.
As a cheap programmer, I appreciate the consideration, as I like to feel I have some utility. But as an entrepreneur, I think it's a bad idea.
As a not-so-cheap (by local standards) programmer, I'd have to agree with this assessment. Sometimes, customers will ask if it's possible to reduce the budget for a contracted piece of work by getting some of their internal staff to do parts of it. I've tried to make this work, but it basically doesn't in most cases, for the reasons you mention. On the occasions I agreed to try it, it would have ended up more expensive, even when assuming internal staff time to have a cost of zero. Fortunately I agreed to try it only on the condition I could bail out and do it all myself if it wasn't working. Which I did.
I realise this may come across as me being arrogant or unable to work in a team. I can't with good conscience pass judgement on the former; I am however frequently contracted as an extra brain and pair of hands on projects with people of comparable skill who could do it without me, save for the project's time constraint. This generally works very well.
It's conceivable that the model might work if the skill gap isn't so big. Presumably that makes the programmers less cheap, and the scheme less attractive. Plus, they could probably muddle through without me, thus never feeling the need to hire me in the first place. Which, I assume, is why this has never happened to me.
I concur, a sort of an apprenticeship program would be quite useful. If an expert can guide 1-3 people to do most menial tasks, it would serve the dual purpose of getting stuff done and educating a lot of interested people.
Currently we have university projects, internships and the like. However those are often slow to react to technology changes, or are too rigid and lacking proper employee orientation procedures.
It is a nice pipe dream to have a sort of a board where one could find a mentor in a particular subject, while working on a real-life project that shows all the dirty stuff that most undergrads are sheltered from before they enter the job market. E.g. topics of the "I'm doing a Django project and I could use some slaves to do this, this and that" sort.
Taking the idea to software, maybe it wouldn't hurt to hire cheap programmers as long as they're following the directions of an expert.