It's an interesting idea, but the truth is that being a mechanic and beeing a builder are two different things. Many mechanics build beautiful, solid experimental aircraft. Some will just drill holes through their fingers. The A&P exam does not emphasize the same things required in building an airplane, and schools are training and educating people to pass the exams.
Then, of course, comes the fact that if you simply buy the kit and have someone else build it, you are not going to be the builder of record anyway, and won't qualify for the repairman's certificate (unless you lie on the forms about who built it). So you might as well expand your search beyond A&P schools.
The good news is that there are thousands of experimental aircraft out there, many of which change hands - and usually for the cost of the materials it took to build them. If you want an airplane, buy an airplane. If you want to build an airplane, build an airplane. But there's no need to complicate things by having one built for you.
Paul