Not having a way for web apps to communicate a call to action dramatically reduces engagement with this feature, no doubt. The only way I can see this from Apple's side is they see it as a feature for Safari users, not from the platform side for the web.
From Apple's standpoint, when you put yourself on the user's homescreen, that is a deep connection between that app and the user. Apple spends billions in each finding new ways to enhance and enrich that connection. IMO, their _belief_ is that building a native app to take advantage of all these rich and engaging ways is the best way to build deep connections with your (developer's) users.
Being an icon on the user's home screen is where deep connection begins, not ends. You might add a today widget, you might want to send notifications, you might want to add AR experiences. You might want a Tablet experience and allow hand off between these devices. Apple is invested in becoming a deep level of importance in a user's life. They want to share as large of surface area with 3rd party developers as they can. It would be irresponsible to promote an API that made developers have to start from scratch when they decide they want to go deeper.