Most of the OEMs that form the bulk of android shipments probably don't even use Qualcomm. See Samsung's Exynos, Huawei also makes its own chips and then there is MediaTek.
Seeing as Microsoft supports Qualcomm exclusively for Windows 10 mobile(and WP before) Id have thought they could get in early on latest chipsets from Qualcomm. Given though they need powerful silicon to drive continuum and imaging prowess that has come to associate with Lumias.
Qualcomm still gets vastly more business from Android OEM's then Microsoft phones.
Samsung's Exynos processors are exclusive to only a select few phones (and in the past those phones have only been available in Samsung's native South Korea...the Galaxy S6 is the first phone available worldwide with an Exynos, like the Tab S tablets were...even the LTE Tab S' used Qualcomm processors).
Huawei's Kirin chips are only used by Huawei and Honor, and not even all of them, only a few.
MediaTek is used mostly in Chinese OEM's phones, and you don't see them that often elsewhere.
Qualcomm (even after the bad rep from the Snapdragon 810) is still by far the largest chip manufacturer out there. If Samsung started producing Exynos processors for other OEM's maybe they'd have a chance of taking Qualcomm but Qualcomm could lose Microsoft and probably not care.