Kotegaishi needs kuzushi to work. If you accomplish that with atemi I can think of better things to do than switch to that particular technique.
I think we have gone beyond the realm of what can be discussed online. I know what I'm visualizing, but I'm not sure I can convey the nuances accurately.
The short version is that, in our approach, a strong irimi is the starting point of pretty much every technique, and that includes both a focus on uke's center and at least the threat of an appropriate atemi. The resulting technique then depends on what uke does: in kata practice, it's uke's responsibility to respond in a way that allows nage to complete the prescribed technique.
If we're not practicing a specific kata, then my goal as nage is to get uke on the ground and neutralize the situation as efficiently as possible, which may or may not involve kotegaeshi but *will* involve a strong irimi.