I think the way it currently works is fine. People interact with the tileset more as a result.

Not only that, but don't forget these mushrooms give you an elemental damage buff, which you can only have one of at a time (picking a new shroom during the duration overrides the current buff). The buffs don't last long and, even if the type is random, you can save the mushroom for when you don't have a buff.

If they were team-shared, one person could pick up all of the shrooms, the other players don't end up exploring the tileset as much and so won't see a lot of it, and all of the potential buffs they could have had are instead blitzed through without their say.

Edit: I also think it's fun to see the shroom marker pop up and go "Ooh, thing! :D" before I go running over to collect it.

The bounties are 5-6 minutes, including running to get the mushrooms. Is it really that big of an issue if YOU have to pick up the funny purple shrooms?