Quirlies can be owned for the purpose of role-playing with other members, as the lore is already well built. You can also participate in art events which require you to draw your quirli doing some things to get rewards.
I'm hoping I won't get a large herd of them, since I want to focus on leveling up 1 recognizable quirli. In fact, the whole purpose of creating a Toy House was to keep track of my quirlies' chimes (or levels).
Update: I pretty much immediately gave up and will probably end up with a lot of them lol (27th of April 2021)