It seems like both Yom Kippur and Tisha bAv, for different reasons, would ideally be two days long. However, we just do one day because we are unable to fast for two days. My question is, why cancel the whole second day when we could just not fast? Why not have a second day of Yom Kippur and Tisha bAv where you can eat, but all other prohibitions and practices still apply?

The concept of a second day is rabbinic, and they decided to decree only regarding holidays and not heavy & sad fast days, which would be too much to ask from God's children. They only decree that which the masses can fulfill beneficially and gladly.