Mordekaiser should be able to control Baron, and here's why it would work

Why can he control Dragon but not Baron? Why go only halfway in a mechanic such as this?

If need be, just make him have to use his ult to control Baron. Baron is stationary regardless, so, it's a tactical decision. The damage from his ult would also make him a viable jungler because of his secure potential.

Additionally, you can make it so that if the enemy team secures Baron, Morde doesn't get a ghost. Wasted ult. Again, tactical decisionmaking.

There's no reason to not let him control Baron.