There are many fruit trees that are “bushes” like the aforementioned lemon. You should have chopped that papaya in half. It will come back with 5 times the foliage. Papayas do need a male and female plant to make fruit, however. Papaya is NOT a tree, it is herbaceous like a banana. For the record you can almost always chop a fruit tree way back and it will return with more foliage. For example, on my mulberry tree I chop every branch in half in the fall. You gotta be brutal.
Note: there are a lot of mango varieties that were modified to be “balcony” trees.
Love mulberries! I know I could have cut it back but I had no room for two trees, barely that one. It’s been happy at the botanic gardens.
PS - I’ve been cutting my pawpaw trees (4) back for years. And they have branches out beautifully.
I remember my Grandpa whacking his under-producing apple tree on the trunk with a bat!
Never did get the skinny on the reason it worked, but he swore by it; we never lacked for apples when I was growing up.