I don't, unless certain criteria are met.
There is a consumer-friendly side of apps that is often overlooked in these types of conversations: generally, I get to decide when to update my apps, and the developer can't uninstall their app off my phone without my permission. Moving from apps to the web shifts the balance of power even further from user to developer.
There are some apps (that require internet access) for which this is not true. For those, I share your sentiment; spotify has no reason to be an app. It's also possible to implement this amount of user control with the web, by caching the full version of a page, when you add it to your home screen (for example), and only replacing it after an explicit prompt (as a setting, ie auto-update).
Until that happens, though, I don't wish for the death of app stores. Especially, f-droid is a great ecosystem.