There are several ways you can approach 'solving a problem'. You can iterate, trying one proposed solution after another until you find one that works. This is (supposedly) how the light bulb was invented. The drawback to 'iteration' is that you may find a solution that works but is sub-optimal; there's another solution that's better, but you didn't find that first, so it didn't get adopted. Again, this may be true of the light bulb. Also, because you have found a solution, it will be applied to every instance of the problem, for some of which it will work excellently and for others of which it will barely work at all. Of course, if there's only one manifestation of 'the problem', we don't have to worry about that.
For that case where 'the problem' exists in several versions, there is a better way: massively-parallel trial-and-error. Set n teams to work solving the problem. As solutions begin to be put into practice, we should expect to see at once that most solutions are unworkable, some are acceptable, and a few are remarkable. The unworkable solutions can be discarded, the acceptable solutions can be improved, and the remarkable solutions can be adopted. We wind up with several solutions that can be applied to various manifestations of the problem. The drawback to this method is that it is expensive because every proposed line of research must be funded up front. The costs that might have been avoided because we found that initial (possibly sub-optimal) solution and stopped looking are going to be spent right now. We're going to examine every plausible solution and we're going to pay for the examination today. We actually have laboratories where this type of problem-solving can take place. They are called 'states'.
In fact, save for a few issues already addressed in the Constitution, most of the country's problems are supposed to be solved using this massively-parallel trial-and-error method. Each of the states is supposed to solve its own problems of health, education, and welfare (among other things). Fifty potentially different solutions to each problem, each solution funded not by a gigantic federal bureaucracy but by the states themselves. After a reasonable trial period we would be able to discern that the Iowa model for education works easily as well as the South Carolina model and that the Idaho model is a catastrophe for everything beyond kindergarten. Before long, Kansas would drop their solution in favor of the South Carolina model, and Idaho would adopt the Iowa model. Over time, each state would move toward better solutions and away from poorer solutions, a process we regard as 'improvement'. How much better this than a 'one size fits all' solution imposed by the federal machine onto places and conditions for which that single allowable solution may or may not be workable?
Impossible, you say? Up until very recently, this was the way we dealt with wide-spread problems. Some states did better, others worse, but all did as well as they could given the resources available. Why don't we still do this? Perhaps the answer was best enunciated by Thomas Sowell:
The first lesson of economics is scarcity: there is never enough of anything to fully satisfy all those who want it. The first lesson of politics is to disregard the first lesson of economics.