[quote=@Peik]
<Snipped quote by Chrononaut>

For some reason I can't see them giving a fuck.

The Oblivion Crisis was led by the Lord of Destruction after all.
[/quote]

They might have interfered if he was actually able to succeed, Jyggalag was an older prince turned into Sheogorath because the other Princes were scared that he became too powerful. The Lord of destruction destroying the entire known world might be "too powerful". Who knows, maybe they empowered the protagonist during all the optional quests because it would possibly help him stop Molag Bal.

On another note, Hircine would care because if Mehrunes Dagon destroyed the world there could be no hunt, the only thing he cares about. Molag Bal couldn't dominate that which was destroyed. So really it depended on whether or not Mehrunes planned to destroy ALL THE THINGS. Because the Princes do tend to care about their specific aspect.