I think you may be underestimating the overlap between smartphone and desktop functionality. Take a look at the home screen of your smartphone - what percentage of those apps are also available as a web app? For me that figure is about 80%.
Amusingly, for me, there's exactly one app with a web equivalent that's not a preinstalled Google app (a weather app). The rest all are either doing things with hardware that the web doesn't know how to access (accelerometer, microphone, camera, FM radio, SMS, cell, raw network access), or apps for managing data on the phone itself (contacts, image gallery), or services with no web equivalent (Steam, Lyft).
And that's just the thing: if your app can be done on the web, you're already going to do it on the web, because there's not a platform on the planet that won't automatically have it. If the website that you already have doesn't perform well enough, then you make a second app while you wait for the web to reach parity.
You're going to think I'm weird, but I don't use the Facebook app, I use the site. I don't use the Twitter app, I use the site. This isn't some philosophical choice on my part, I really just can't be arsed to take the effort to search for yet another app on the app store, and then fret over the implications of approving yet another set of meaningless permissions, and then resign myself to endure yet another app pestering me to update it for the rest of my days.
I accept that there will always be a place for native apps. The web is slow to pick up on new bits of hardware and new modes of interaction, so native will always be ahead of the pack there (though Mozilla is at least attempting to prepare itself for the Oculus Rift with a big push for VR on the web). It's a conservative platform. But once something is Good Enough for the web, you need a very good reason to dislodge it.
We are clearly polar opposites because I love native apps ;) For example you might think The Economist was perfectly suited to a browser web 'app', but I prefer the native Android app because (a) it notifies me when a new issue is published; (b) it downloads the content offline; (c) it is fast to navigate and has smooth animations between pages.
I think we've been talking about two separate issues:
1. Do a significant proportion of apps need to provide the same functionality on both a smartphone and on desktop computers? Here I think the answer is yes. Twitter, Gmail, weather apps, maps, image gallery, music streaming, games, banking apps, youtube, etc. provide essentially the same feature set on both devices.
2. If an app needs to run on both smartphone and desktop, should it be native or a web app? Here I think the answer is not so clear-cut. Certainly in the past 15 years it was true that "if your app can be done on the web, you're already going to do it on the web, because there's not a platform on the planet that won't automatically have it". But will that still be the case in 5 years time? The choice of platform for a new app depends on more than just the potential number of users - the usability and development cost also matter. Let's say I expect to produce a web app, an iOS app and an Android app - is it really worth the extra cost to produce the web app if I can cover 95% of the potential user base without it?
> But will that still be the case in 5 years time?
By 2020 I don't expect any new platform to arise that both lacks a standards-compliant web browser and manages to enforce the lack of such a web browser. I also don't expect any existing platform's browsers to regress from the degree of standards compliance that they have at this moment. There do exist several scenarios whereby web standards could stagnate over this time period:
Scenario 1: A major platform allows only a single browser, that browser being produced by the platform's parent company, and drags its feet in order to impede the standards process and promote native app development over web app development. The obvious potential candidate here is iOS, with Safari being the last major browser that has yet to commit to an "evergreen" model whereby features are quickly and regularly released. However, if ARC were to ever pose a threat to Apple's app model such that they could not somehow counter it with crippling technical constraints, it would be in their best interest to rapidly advance Safari to feature parity with other browsers. In other words, if Apple were ever faced with the decision of empowering the web vs. tacitly empowering a platform backed solely by Google, they're always going to choose the web.
Scenario 2: Chrome becomes dominant to the same degree that IE6 was once dominant. At this point anything that Google decides to implement (or to not implement) would de facto determine web standards, and just like Microsoft of old they could choose to leverage this power in order to advance a proprietary platform under their exclusive control. This is largely kept in check by Chrome's inability to exist on iOS as anything other than a thin wrapper over Safari, a situation that is unlikely to ever change (at least, I don't see any business motive to Apple making such a thing possible).
Scenario 3: Mozilla somehow loses its seat at the standards table. In the short term it may seem like Firefox can be ignored to a degree, but in the long term Mozilla is the Bismarck that keeps web standards moving forward in ways that are seen as beneficial to a majority of the vendors at the table. As long as there exist platforms with sizable userbases on which Firefox can be installed, it is in Mozilla's interest to advance the web as quickly as possible while convincing two of the big three to play along in order to undermine the remaining mutual competitor (and hence indirectly gaining an influence over that competitor's closed platform, using the browser as an attack vector). Mozilla's recent contract with Yahoo will sustain their efforts at their current levels for at least another five years, but its fate beyond that time will depend on how well FirefoxOS does at keeping Firefox from being locked out of the increasingly closed platforms of the future.
Given all of the above, I think it's safe to say that the web will continue to evolve rapidly for at least another five years, and the inexorable advance of mobile hardware will continue to close the gap between native performance and web performance (with projects like Mozilla's Servo designed to accelerate the closing of this gap). In the meantime, the biggest hurdles are the process of web app development (sorely lacking compared to native development, though there appear to be tentative steps in the right direction) and the unanswered question of how to make payment on the web as frictionless as it is on mobile (seriously, someone start working on this).
Yes the three scenarios you mention are unlikely, and I agree that the web will continue to evolve rapidly for at least another five years. But isn't it possible for web apps continue to close the performance gap yet still lose their dominance as the 'first choice' for startup development?
For example, perhaps Google will make it much easier to port an Android app to iOS, similar to the way SWT makes it easy to write a single app that uses native controls on both Mac and Windows.
This Android+iOS app could then run on Windows, Mac, ChromeOS, Linux, Android, and iOS. Suppose that the cost of developing such an app is roughly equal to the cost of developing a web app. Wouldn't startups be tempted to choose this platform over a web app?