Because it is hard and an active area of mathematical research. Which relates to the second question, yes, QED is the most accurate physical theory ever created

Because it is hard and an active area of mathematical research. Which relates to the second question, yes, QED is the most accurate physical theory ever created and its unique predictions have been validated over the past 50 years. The issue is that physicists are a little hand wavy with mathematical formalism, so mathematicians are left trying to formalize , and that is worthwhile because of how effective it has been as a physical theory