I know what you're saying but elegance is not simply an aesthetic concern.

The value of a proof is not only its conclusion but also the insight that it provides through its method.

The goal of mathematics is not to prove as many theorems as possible but rather to gain an ever deeper understanding of why certain statements are true. The way that something is proved can be more or less useful to advancing that goal.

As an example the elementary proof(s) of the prime number theorem are just about as famous as the original proof. Sometimes the second bite of the cherry is even juicier than the first.