Why No Rivalry Trophy?

I am watching the Minnesota-Wisconsin football game. Oldest rivalry in Division I College Football. They play for the Paul Bunyan Axe, as pictured above.

How come Michigan v. OSU do not have a rivalry trophy? What about Michigan v. Wisconsin, OSU v. Wisconsin, or PSU v Michigan?

I understand that if THE GAME is too big to have a measley trophy. But why not these other games? They are pretty big - as of late - and I get the sense that none of the aforementioned Big Ten programs like the UW program. What a perfect relationship to have a rivalry trophy!

What does it take to create a rivalry trophy? Can't we just make something up?

C'mon, people! I think the Big Ten should just be about rivalry trophies. Let's have something for every match-up.