Neglecting the core product to pursue a phone OS that was very unlikely to succeed was bad for the company.

Not only for small companies. Microsoft threw billions had at it, bought a phone manufacturer, had a pretty nice phone OS, had a name in business, and was years earlier then Mozilla and Canonical. And they failed miserably.

(Of course, the whole WP7 -> WP8 transition was handled badly, but it shows that even a company with extremely deep pockets will fail to capture significant marketshare.)

I think Windows Phone failed primarily because Microsoft did not take early steps to cultivate a competitive app store, which they probably could have done back then -- these days, it would probably be impossible. They also didn't have very many desirable flagship phones, especially compared to the iPhone and the Samsung Galaxy series.

Microsoft's failure was partially self-inflicted, but Mozilla and Canonical would have had no chance even if they did everything right. They don't have the scale, and they are now up against app stores with millions of apps. It doesn't matter how nice the OS is if it can't run Facebook, Snapchat, and a bunch of popular games on day one.

A dedicated desktop OS is capable of rich and complex interactions. Could a mobile 'desktop mode' ever match such capabilities?

I'd rather have a dedicated desktop OS that maximises features suitable for the desktop hardware it runs on. Not an OS that has to lower it's capabilities and interactions to match the smallest device it runs on.