I cant see how web apps could ever compete with native apps. Native apps monopolise both the desktop and the mobile.
Web apps on the other hand are popular only because of the popularity of the internet. Its just a convenience nothing more. Not that you cannot make amazing web apps.
However web dev has some serious issues, huge fragmentation, badly design libraries, extremely limited libraries, improvements are slow to come, performance is really bad and much more.
Take the field I am working on , game development. We were hearing some time ago that web would be the future for games, that facebook and other social media website would be excellent platforms to entertain people. It never happened. Its 2016 and the penetration of the web games is like 6% and not only that its also shrinking to oblivion.
Its not the first or the last time we hear huge promises by web developers , lets not forget the massive failure of the Cloud. The idea was that all application would move the cloud , you will no longer need a powerful computer, everyone is happy and free. Never happened. We got some cool cloud apps like Dropbox and Google Docs but that is pretty much it. Cloud has died of as a hyped work and life goes on.
My advise for web apps , is to stick to what they are doing best, augmenting websites. They dont have the technology to compete with native and native moves too fast for the glacial slow implementation of web standards. Lets not forget how it took forever for HTML5.
Node.js another thing supposed to dominate the native apps, did well on the server front and that was pretty much it. That died off too.
The new hype is web assembly, the usual, huge promises, big dreams. That is also going to deflate. Though obviously useful.
Native apps also start to penetrate the internet lately. Some mobile apps for example are mostly websites wrapped inside a native app. Apps for forums, blog sites, picture sites, e-shops etc. Users prefer them because they are more smooth in interaction and much more powerful.
My prediction is that at some point web apps will go extinct and be completely replaced by native apps. Browsers already have grown monsterous. Firefox needs 1GB just for a few tabs. Other browsers are not much better either. The web technology will merge with native technology , some of the web technology will fail to survive the assimilation but most of it will be around for a long time for legacy reasons. On the other hand that will mean that web apps will now have direct access to native technologies and many limitations and performance issues will be lifted.