At the risk of repeating Ision's ideas, here's how this "wonder-weaning" strategy works for me, and also extends to the selection of civ traits.
The idea of avoiding wonders to improve gameplay has merit if taken as intended: not to handicap yourself but to learn which things you can work around and which will really benefit your civ in a way that another strategy couldn't. For example: do you really need a barracks in EVERY city, or just the more productive ones? If you can specialize your cities so that some produce land units while othes focus on sea/bombard units, then Sun Tzu's becomes less critical.
Similarly, you can take the same philosophy with civ traits. Think what trait seems to you to be most important, then develop a game style that compensates for NOT having that particular trait. I used to think Scientific, Religious, and Industrious were the best traits. But now I use forestry tactics a lot more, especially when building temples in ancient era, buy/capture more workers than I build, only have about 2 revolutions per game, and buy/trade tech so aggressively that I do better when my RIVALS are scientific. Hence Agricultural and Commercial traits now seem more advantagious to me, since I can't seem to find play tactics that compensate for the benefits of those traits. (Increase in the raw input of food/commerce).
Back to wonders, I of course still like to build wonders in my games...I'm just more selective about which ones, and look at the particular context of each game. Sometimes Magellan's is crucial for shortening the ferry distance of a critical crossing by one turn. Sometimes, in a luxury-poor context with a non-religious civ, the little boost given by JS Bach's is quite nice. But rarely do I find a particular wonder, at least pre-ToE, Hoover's, and UN, is a "must-have". Which is a good thing, because on higher levels the "must-haves" are most often out of reach.