It's been stated repeatedly why this has been done, on TAZ. When we called it "Mobile Push" people thought it excluded Desktop. When we called it "Web Push" people thought it excluded Mobile, and not as many care about desktop. Then we went with "Mobile/Web Push" (MWP).
As of the last release, we made the Mobile Suite which is centered around turning forums in progressive web apps, and merged in the code from MWP as push notifications are obviously a core part of that experience (technically different products, but one merged into the other).
You are thinking of the discontinued native apps, which are unrelated to this product. At that time we made a breakthrough that allowed us to substantially reduce the forums' cost of deploying that native app without requiring much technical knowledge from the admin.