I've had a slight change of view over kotegaeshi over the past few months. It is often done with the hip going in very quickly and a large circular throw. This enables the counter (as described) with the kick to the head - also, if the kotegaeshi is too slow it results in uke either hitting nage with his other hand or just charging in to nage.
An alternative is to withdraw ukes arm to the side (as you would normally, turning him around). But well before his centre is lined up with his own wrist you put kote-gaeshi on. This doesn't look as pretty and usually results in a backward ukemi rather than forward ukemi for uke. However it prevents being kicked, or hit. It also prevents uke getting control of your wrist for the counter, as his centre never comes in line with his arm (and therefore he is weak). In terms of real application, you cannot get a throw out of this and you would have to either cause them to sit down with the pain (unlikely I think) or break the wrist.