Personally I don't find too much of an issue with the position of the box button, but could see where this might be annoying.
The horse/drasine/etc can be used while carrying the bounty box, but in an unintuitive way. You have to drop the box, then hop on your mount, then run over the box to 'pick it up.' Same with drasine - drop the box on the rr track and then run it over to pick it up. Using the reactive glove button to hop the drasine track has similar results, as does using reactive glove to dive in the water.
I feel like it would be super slick if we could use bombs and arrows to fight baddies. Especially considering how many friggin spiders, rats, bats, etc are required for the bounty. The time it takes makes a lot of people just ignore certain critters when it comes up in their bounty.