Italians eat pasta al dente. Since pasta originated in Italy, it only seems natural that it be prepared the way it was meant to by its creators. With pasta being an Italian food, other countries who serve it were taught how to do so by Italians.
The texture of al dente pasta is not soft (or “mushy”). Pasta is meant to keep its correct form, not completely break down like you spoke of in your description.
There is also belief that pasta actually has better health benefits when it is cooked al dente instead of cooked too long. The belief is that the GI rating of pasta is between 30 and 60, with al dente pasta being lower on the GI scale.
If pasta is cooked al dente, it takes longer to chew, longer to digest, and does not spike blood sugar levels as more-cooked pasta does. As I said, this is a belief. I can give you the reference I found this particular information on. If you want to check the authenticity of their claims, you should do so. The reference link is: http://www.popsugar.com/fitness/Al-Dente-Good-Your-Health-878080.