OP says open source is a reformulation of free software.

Stallman created free software and is distinctly against open source, which is more or less free software but without the philosophy, the concern for user rights [1]. Associating RMS and his printer with the purpose of open source would somewhat be a mistake / a faux pas (but would be nailing it for the purpose of free software!).

The purpose of free software is user freedom (and not the cooperative development). The original purpose of open source is selling the idea of free software to the corporate world by making it less scary to them, by trying to remove its political part. [I suspect the people who created open source might have been sensitive to the user freedom aspect and wanted to convince corporate to do free software for this reason but thought that hiding this part was a good strategy [2, 3]. I personally think this was a fatal mistake: nowadays, although the infrastructure is mostly open source (and has been succeeding in this regard), end user facing software is still mostly proprietary exactly because software companies don't think they ought to do free software.]

I don't think the cooperative development part is in the purpose of open source. In any case, the open source definition and the free software definition don't concern themselves with this and are purely about what you can do with the code.

Of course open source development models are intimately bound to open source and free software but and were one of the things sold to corporate as more efficient.

[1] https://www.gnu.org/philosophy/open-source-misses-the-point....

[2] https://en.wikipedia.org/wiki/Bruce_Perens#cite_note-18

[3] "It's Time to Talk About Free Software Again" http://lists.debian.org/debian-devel/1999/debian-devel-19990...