Well, let's examine this a bit.

Let's assume for the moment that such a thing can exist. Why does it not exist?

What do we know about free (as in speech) software?

- It tends to be written by people on their own time, or funded by companies that want to make sure it continues to exist (though generally, AFAIK, such companies only support existing projects; they don't fund people to create new open-source projects that wouldn't be under their control).

- Largely because of this and the Unix philosophy, it tends to be created as individual projects each made to do one job well, which can then be glued together to do larger jobs.

- It tends to be much less user-friendly than commercial software.

Putting all this together, it is not too hard to see why there aren't widely-adopted free-as-in-speech phone OSes. A phone OS is a large project, which needs to bring a lot of smaller components together within it in a consistent and predictable way; it is a very significant undertaking, requiring a high number of person-hours of work to make usable; and vitally, in order to be commercially viable, it needs to be user-friendly.

So it is very likely that such a project could, theoretically exist, but in practice never will, unless some very wealthy person or group decides to fund its creation without hope of commercial ROI.