My fear is that by the time Microsoft can get the apps ready for Continuum, Android or Apple (well, most likely not Apple as it'd butcher sales of their own products) will come out with their own version of this feature.
I'm doubly-confused by your comment. For starters, Apple is notorious for cannibalizing its own products again and again and again - just look at the iPod, the iPad/iPad Mini (and especially the iPad Pro now), the MacBook... They've done this in many instances with their software as well. If there's any company that refuses to challenge their own existing lineup, it's almost certainly
Microsoft, especially in the Ballmer years. Why do you think Windows Phone has been nothing but a commercial failure? (And remember the Kin?)
Furthermore, Apple's Continuity is by far the best example of what Microsoft's Continuum is meant to deliver - a seamless experience across devices - that works well, and that you can actually have today. Apple's approach is different, since it's desktop-first and mobile-first operating systems that underpin the platforms, but the feature set you get - same app on multiple devices, synchronized files, passing over work, universal notifications, and so forth - are identical. I frequently start writing things on my iPhone and effortlessly continue them on my desktop. Or pass calls from my phone to my laptop. Or open a webpage I had on my laptop, and keep reading it on my phone. Or buy an iPhone app and have the desktop version waiting for me. This is not the future for Mac and iOS users; this is two years old now.
With the upcoming OS releases in the fall, it gets even better. Now my watch unlocks my laptop for me. Now developers can do a lot more over iCloud between iOS and macOS apps. Now more of the features of both platforms, such as Siri, are universal. And on and on.
Frankly, Microsoft has been parroting the idea of "one platform for all devices" for nearly a decade, and
every single attempt to realize that vision has been a failure. Every single one! Vista on tablets was a failure, the original Windows for smartphones was a failure, Windows 7 on tablets was a failure, the new Windows Phone was a failure, Windows 8 on tablets was a failure, Windows 8.1 on
desktops was a failure... They're
still failing at it right now, too, because they can't get a sizable chunk of people to download Windows 10 even when resorting to stuffing it down people's throats, and because they have a nearly non-existent mobile user base,
and because they have a convoluted approach for developers for Universal Apps. They've also been remarkably inconsistent about the tools and strategy for mobile, which is about the worst invitation you can give to a developer when asking them to sink time into supporting an unproven ecosystem.
Meanwhile, Apple's
already providing the benefits of that vision, in an effective way, for several years now, that developers have been building upon. I have no idea why PC-only folks haven't started revolting over this
Microsoft has been pulling a Molyneux for a decade with respect to this.