I want to give my feedback here from the other side.
Whatever you do, absolutely do not make tasks added to My Tasks public by default.
When I first moved my team to Asana over a year ago, I actually wrote a comment here requesting that My Tasks were public, since I thought it wasn’t optimal that I couldn’t browse such tasks on my team’s list.
But I soon learned that it’s much better to default to private, then let people make them public as appropriate.
I’m not sure if this is a bug or not, but today, the IOS hard press quick add New Task is defaulting to “Public to My Tasks in [company name]”. It had always been private. Wow, this is really bad design. It might just be a bug though (I hope), because those tasks do not sync properly with the desktop app, they still appear to be private, and after I create the first such task, additional tasks created the same way are correctly set to private.
I jot down tasks on my phone all day as they come to me, then I process them later and assign to the right projects/people with the right permissions. Default public on all tasks is ridiculous. E.g., a manager might want to make a quick HR note about a worker to follow up on later, and that is not meant to be shared with everybody in the company.