Well think about it. It puts to much strain on his body and wouldn't really help with that much strain. It was already not working with Frieza, so imagine with even stronger opponents. Anyways, he has super Saiyan which is better and doesn't put strain on his body. Well except ssj3. Also, if he used Kaioken while super Saiyan, it would be an INSANE amount of strain on his body. He was able to do it against Pikkon because he was dead and his dead body can handle much more...... Hope it explains. And sorry for the big nerd talk!
Well, yeah, but the fact is, a Super Saiyan transformation multiplies your power by 50.. And yes, I know that Goku can't multiply the Kaioken to high in transformed states.. Then again, from the Saiyan Saga up towards the end of the Frieza saga, through intense training, he went from only being able to go Kaioken x2, to being able to go Kaioken x20.. It can be theorized that if Goku trained much more, he would be able to use the Kaioken no matter what condition..