You have the ability to disable just browser push notifications, at least for Android. I actually find notifications useful, but they can quickly become useless if you are receiving a lot of irrelevant notifications. If you disable all notifications on Android, you wont get things like calendar reminders.

Although it can be useful for some web applications, I kind of wish that push notifications were not added to browsers. Most often they are just abused to spam users. The pop-up you get while going to pages asking you to allow push notifications is also annoying. I have started to disable notifications in all the browsers I use on mobile and desktop.