Mathematics often does apply to the real world, but that isn't the goal. Physics is about the study of the real universe. If you want to call string theory a branch of mathematics I'd be fine with it, but they keep trying to claim they are physicists and that puts a higher bar on what we expect from them.

Of course physicists sometimes do make wrong predictions and it can take some time to figure out the hypothesis is wrong. However the goal is always to make something they can test to prove the hypothesis holds, which string theory has so far failed to do.