All things that create lift, lift the wings—and you need them all for efficient flight. The Bernoulli effect is one thing, but does not produce the main lift force in many circumstances.

Aircraft with symmetrical wings fly just fine, and most aircraft can fly upside down. So you don't need the Bernoulli effect. Exploiting all the effects gives you more efficient planes though

Mandatory XKCD: [1]

[1] https://xkcd.com/803/

You need a lot of power to lift an aircraft without the Bernoulli effect. That's why all planes take advantage of it.

About 20% more power, provided perfect conversion. A lot? You tell me!

also discussed here https://news.ycombinator.com/item?id=40835223