The wavedash is far more important then being able to hit Jump + Direction + Shield
The "technical aspect" of wavedashing is minimal, and is not important (it wouldn't be any different if there was a "wavedash button", or a third control stick on the controller).
It's used as a momentum canceller, momentum modifier (dash>wavedash>dash, momentem changed depending on which direction you wavedashed back/down/forward), "bait" eg move forward, wavedash back just before an attack comes out, your opponent launches an attack, whiffs. Also gives more defensive maneverbility -- your attacker has a harder time predicting where you are going to be if you are dashing and wavedashing heaps.
So it's quite an important technique, and it's more relevant to gameplay then l-canceling is (which is argued as the most useful technique -- and I'd agree, yet wavedashing changes the options of the game, L-cancelling only allows you to maintain momentum in a binary way "yes / no you recovered fast enough".
Another reason "technical skill" is cited as a big part of Melee is because learning combos is a) fun and b) challenging and c) awesomely tricky with DI & ASDI and teching. Since there aren't as many combos to learn a lot of gameplay is "missing".
If you look back up at the momentum paragraph, you'll see that you don't have nearly the sort of options in Brawl as you do with Melee's wavedash. Some characters have useful/special techniques in Brawl that give them more options (Squirtle sliding for example) -- Melee's universal wavedash meant everyone had these things available to them, making it "balanced" in the sense that everyone had access to it (not everyone has access to infinite chain throws!!)
second edit: Similarly, and I'm not being rude by suggesting this, you could play more Melee and see the difference the wave-dash makes first hand.