Do I really need a $750 fly rod?

Emphatically, no.

Are expensive rods really better than cheaper ones?

Cosmetically, without a doubt.  In terms of casting performance, yes, usually.

Are top-end rods actually worth the money?

This ultimately depends on what you mean by “worth.”  From what might be called the “cost/performance” ratio – – if it is even possible to quantify such a thing – – the answer is probably no.  A $750 rod will not cast five times as far, or five times as delicately, or five times more accurately, or five times anything as a $150 rod, though it will almost certainly feel and perform better.

But might you enjoy owning and fishing it five times as much?

Quite conceivably.

In the end, if it’s worth it to you, it’s worth it.  And only one person can make that decision.