My reading of it is that it is a combination of things. Firstly watches often have a better view of the sky rather than a phone on an upper-arm band or in a pocket on your back. Combine that with GPS aerials which may be obscured by electronics, positioned best for use in cars etc on phones, and the GPS watch is a better device.
Secondly, and I think this is the most important, the software / firmware on watches is written to help support reporting of a pace profile which reflects the way people run. I could be wrong about this, but I think the Garmin watches (for which I have experience) do some interpolation of the points in software, rather than just accepting the raw GPS data point that has been received.
Thus when GPS trails are reported from watches, whilst they are still a series of dots joined together, they have more of a tendency to report a smooth(er) more realistic pace and route. Whereas often running apps on phones seem to provide a jerkier output, which makes me think their software either doesn't do a job of smoothing, or does a worse job.
And finally I think what you say about phones being multitasking devices can contribute. I don't know about the lottery approach to getting access to GPS, but certainly they are doing a lot more than a watch is simultaneously.