That was my point with "when it's going to the same app". Messages from SMS and iMessage both show up in the same "Messages" app, and are indistinguishable from each other. So it doesn't matter if you're getting spam only from SMS when the app is still lighting up all the time.
My point is that this isn't exclusive to iOS; if you move to Android, that SMS spam isn't going away. Unless you can mute Android's SMS app because you receive 0 legitimate SMS messages, you'll be dealing with the same problem.
