There's never a need. What is "need" anyway? If you're not competing professionally, then what are your "needs?" Even in fairly elite amateur racing, a prime sprint might win you a pair of socks, and you'll need a whole lot of those to make up for the cost of a fancy wheelset.

As far as the question of "am I fast enough to take advantage of a fancy wheelset", the answer is pretty much always "yes." The notion that aerodynamics doesn't become significant until well over 20mph is nonsense; if you're cruising along the flats at 18mph, a large majority of the resistance that you're battling is aerodynamic. That being said, though, wheels are only a small fraction of the total drag of bike+rider. And since your wheels are already not very non-aero, the gains to be had from switching to a fancy wheelset are unlikely to be dramatic. You might see a few tenths of a mph, but not several mph unless there's something dramatically wrong with your current wheels, like if you pumped the tires full of corn syrup instead of air, or if you packed your bearings with concrete instead of grease.
Everyone can benefit from fancy wheels, but fancy wheels aren't necessarily the first place you should look for speed gains. If you're after speed, and you aren't already using a fast helmet (i.e. something of the Bontrager Ballista sort), and good tight-fitting clothing, look into those first...

On the other hand, what do you WANT? If you WANT fancy wheels, and can reasonably afford them, go ahead and get them. Especially if they're then sort that make a good WOMP-WOMP sound, everyone likes a good WOMP-WOMP wheel. And if you really want to dial in the acoustics, get some latex tubes as well. All tires sound better with latex tubes.