If the engine actually developed power when he advanced the throttle for takeoff, he most likely wasn't actually leaned for taxi. At near-idle settings on the throttle, there is a separate enrichment in most carbs. If you actually want to do something effective at those power settings, you need to get it pretty close to idle-cut-off. Most engines will sputter if you try to go WOT at those settings.
I learned to fly at BJC (6000'). Can't say I ever leaned in the pattern. By then it's way too late. We leaned for taxi and then we leaned again for best power at the run up. With my injected engine now, I can set the fuel flow with the gauge rather than having to manually try to peak things. But still it's more important to set it BEFORE THE TAKEOFF RUN. The extra 800-1000' in the pattern is small potatoes.