There's an edition of a popular webcomic series that poses this question by imagining the convenience of having apps available only when you need them. At first it sounds a little strange, but when you think about it: the mobile web is constantly becoming faster, more reliable, more powerful, and more user-friendly. Most websites you regularly visit probably have a responsively-designed mobile experience that can perform most if not all of the actions of an equivalent app. Not only that, but if you were to scroll through the apps that populate your phone's home screen, how many would you find that you actually use multiple times a week? Better yet: how many apps do you use on a daily basis that aren't reliant upon an internet connection in order to function?
Consider that there was a time when you used native apps on your PC for things that the browser can now do perfectly well, if not better. Music and video streaming services have outdone the humble desktop media player. Most storage needs can be easily and more conveniently handled by a cloud storage service, like Dropbox. And for many, gone are the days of clunky desktop mail clients in favor of having a browser tab dedicated to the task. On our laptop, we witnessed a progression from application icons littering the desktop to a consolidation wherein the browser is a portal to nearly everything. Then the smartphone came along, and independent apps were once again the paradigm.
Sure, you don't need the browser for a calculator or camera app. But you'll likely find that most internet-enabled experiences, such as Facebook or Twitter, have a perfectly capable mobile site. In fact, there are practical arguments to consider for the adoption of web over native apps on a device of limited resources like storage and battery. Aside from the issue of limited storage space forcing you to play musical chairs with your apps, these downloads often come with more strings attached than you may have anticipated. Many people prefer to use the Facebook mobile site over the app, citing that it's a more performant and battery-friendly alternative for their phones.
While the user-experience of the mobile web is mostly powered by a few central principles like responsive design, ease of use, SEO, and speed, when looking towards the future, we've also begun to see more powerful trends on the horizon. Emerging in new development frameworks and patterns is a trend that seeks to make traditional websites more interactive and "app-like." Google is pushing what they call "Progressive Web Apps" as alternatives to native apps. These are apps that are built into the browser, but that are lightweight, fast, and have some functionality that has been traditionally limited in web browsers, such as the local storage of user data for offline use, and push notifications. Google even showcases several of their favorite Progressive Web App experiences.
Clearly, there are still many valid use cases for a mobile app, and I don't think we'll ever witness a dramatic decline in those overnight. However, an app cannot replace your website, and in many cases, it might be more of a difficult proposition for users to justify an app's place on their home screen when they can just navigate to your website when they need to interact with your business. As the mobile web continues to become more accessible all the time, it's easy to imagine a world in which most mobile experiences happen in the browser.