A generation ago, the most common technique for phaco cataract surgery was to use a single incision and a single-hand throughout most of the procedure. That ended up being phased out with the advent of nucleo-fractis techniques which allow us to break up the nucleus into smaller segments. With the original phaco techniques, the nucleus was either prolapsed into the anterior chamber and emulsified (which causes many cases of pseudo-phakic bullous keratopathy, PBK) or it was bowled out within the capsular bag. The bowl-out technique then required skill to get the remaining nuclear shell to collapse on itself before being removed from the eye.
Divide-and-conquer and then phaco chop helped usher in the new age of bimanual surgery where one hand held the phaco probe and the other held a second instrument. You can still perform phaco through a single incision but you must decide how you will divide the nucleus through that single entry site. This video shows a technique that is easy to perform. Note that I still prefer a two-handed approach and there is little, if any, downside to making the extra paracentesis incision to assist.