I don't know what you're complaining about, I play String Bass. Try hauling one of those on a bike! (The pic of Gary Karr pulling a bass behind his bike not withstanding).

My viola in it's case is just about bassoon size/shaped. It rides nicely bungied to the under-seat rack on my recumbent. Really solid.

DH has hauled his French horn in a child's Burley trailer. It's less wonderful, though, a horn is about child-sized, but it's not shaped AT ALL like a child. Still, it works with the net-type bungies.

Oh, and the horn players not being the party type? Tell that to my younger daughter.

Come to think of it, cerebral Elder Daughter plays drums now - she started out as an oboe, but in college switched to percussion, seven (yes, seven) oboes in the band was too much competition, and the percussion section needed warm bodies.