Dolphin is a GPLv2+ application, and the runtime is under a proprietary license. We currently rely on the "system libraries" exception in the GPL to allow linking with the runtime in the first place. If we ship the runtime with Dolphin, it might not be considered a "system library" anymore.
There's some past discussion in this PR, where we made a change to automatically install the runtime DLLs but ended up reverting it: https://github.com/dolphin-emu/dolphin/pull/11068
(this is based off my own recollection of what others have told me, it might be out of date or wrong)