Why retract flaps at go-around?
For the same reason that you don't takeoff with full flaps. Because the climb performance sucks. 

Flaps do add lift, but also a lot of drag. A low flap setting often provides more lift than drag, assisting climbout, whereas full flap offers a whole lot of drag, which is desirable when you want to be slow for landing. 

But a go-around necessitates gaining height quickly, which will not work with landing flap selected. The usual procedure, at least in light aircraft, is to wait until the vertical speed is neutral or positive before retracting flap. This minimises some of the risks you've raised about aircraft control. 

It is often said that a go-around is a period of heavy workload, and managing the flaps and airspeed is not easy. That is why the go-around is a fundamental procedure taught right from the very beginning, and practiced and tested regularly.