Until not that long ago, Microsoft considered open source licenses a "cancer". While they have changed their stance since then, I'm sure they did some major risk assessment and have safeguards in place of the kind a company like Paizo simply isn't capable of. More importantly, the core MS line of products isn't licensed with a license they don't control.
"Not necessarily competitors" makes all the difference here! This is not a minor detail, but a major one. Look at how Wizards of the Coast is framing the issue, and I quote them [0]:
> “the Open Game License was always intended to allow the community to help grow D&D and expand it creatively. It wasn’t intended to subsidize major competitors, especially now that PDF is by far the most common form of distribution.”
and
> “OGL wasn’t intended to fund major competitors and it wasn’t intended to allow people to make D&D apps, videos, or anything other than printed (or printable) materials for use while gaming. We are updating the OGL in part to make that very clear.”
[0] source: https://gizmodo.com/dnd-wizards-of-the-coast-ogl-1-1-open-ga...
Microsoft also publishes software under open-source licenses [0]. The license is short and well-understood, it's not like a large piece of software that might contain backdoors. Also, people trust(-ed) that license.
> If you can do a major rules rewrite [...], surely you have the know-how to design your own license?
Yes, but you'd just end up with a similarly worded license that people don't know. Why spend that money?
Hindsight is 20/20, of course, but I can easily see why they decided against that. Also, Paizo is probably sufficiently funded by now that suing them is a bit dangerous for WotC, as they risk a bad precedent.
[0] Which are not necessarily competitors, but might also not be friendly towards MS.