Why are so many people uncomfortable with the idea that many problems don't have a single solution?

I would conjecture that this is so because multiple solutions makes the ultimate end result harder to see. Multiple solutions denotes multiple variables, and more variables always make a problem harder. A harder problem would inherently be more stressful and more worrying.

Healthcare is a good example of one of these grey area decisions. The American Republican party will tell you that the healthcare idustry MUST be a free market, and the Democratic party will tell you that government intervention will solve all of the free markets problems and provide care for everyone in the US. But both of those inferences are probably false. Many different countries have many different forms of healthcare industry, and none of them are perfect. No country has every single person given the same medical attention as everyone else, and no country has a hundred percent efficient healthcare spending. Each system works differently for each country, but the only way for the US to get to an end result is to attempt a solution. The brilliance of the US should be that if reform doesn't work, we should be able to repeal anything we had put in place, and go back to our old system or even try something new entirely.