They are needed for "closed-loop" since the O2 provides feedback from the exhaust about how the mixture is affecting the emissions. I speculation I heard, however, is that your vehicle will enter open-loop if you accelerate particularly hard, like WOT.
Some mechanic disconnected the O2 on my vehicle. I drove around for 2.5 years not knowing (not fitted with a CEL), then discovered a disconnected harness zip-tied to the underbody... Was getting about 8.5L/100km highway, 10.5L/100km suburban.
After reconnecting, improved to about 7.5L/100k highway, 8.5-9.5L/100km suburban. Also noticed the exhaust didn't reek after a hill climb and a noticeable "shove" when going to WOT. Funnily enough, highway economy doesn't change much with or without A/C, or even when significantly laden.