Why do you say that? In theory much of their value is actually in the sharing/networking aspects. Since they control the backend service and the API, I'd say it could reasonably be a win for them to open source all of their client variants.

They already have an API and which is good. Because in products like this (without millions of admirer) open sourcing the application won't help.

They can open source the application but not add any new developers outside of the company (which wouldn't mean anything, other than good faith).

They can open source it and bunch of people might send stuff in an un-organized way, it never ends good. There are thousands of open source projects some serious usability issues because no one cares and it's hard organise people in open source projects and consistency is the key for usability. So open sourcing projects in this scale, %95 of the time won't be better than what it's.

I can't even recall one successful product that area.

Although publishing more document, samples etc. about API definitely helps.