Why don't Yoo Jae-suk and Kang Ho-dong appear on broadcasts together?

People joke that it's because Kang Ho-dong lost a bet during the "Kung Kung Tta" era and has to defer to Yoo Jae-suk for life, but why don't they actually host shows together in reality?
Since they are both MCs, there are likely issues regarding their appearance fees,
but surely there must have been a production company that tried to plan a show featuring both of them at least once.
With both Yoo Jae-suk and Kang Ho-dong, you can sense an atmosphere where they seem to be somewhat cautious about appearing on screen together.