Are you saying that kaeshi-waza presents itself to you without any training?
It depends on what you mean by "any training."
Without any training in the sense of training that says "a botched this leads to that"? Yep.
All training should be about finding openings. You may not act on them, but you should be noting them and seeing where the opportunity arises for another technique, regardless of whether you are being nage or uke at the moment.
And I do think there is a lot of value in slow freeform practice with a partner that allows these things to develop.