In short I can imagine the trade-off of less-optimal support for some edge cases like these.
Surely sending all these notifications isn't entirely free - someone else posted Snowden receiving 47 gigs of mail because of email notifications.
You could do something like send notifications with some sort of back-off. Send them for 10 seconds, then back off to a minute's worth chunk, then 10 minutes, then an hour.
Then again, I don't have any statistics on how much these external services actually cost, nor how often this actually does happen. Simplest thing is for instagram/twitter to not care, and to point the finger at apple/android and tell them they should have UI to squelch high-frequency notifications.
[1] http://www.statista.com/statistics/419326/us-teen-instagram-...
Bad assumption, given the 90:9:1 rule (99% lurk while 1% participate)
https://en.wikipedia.org/wiki/1%25_rule_(Internet_culture)
1% does mean a lot when you have millions of followers, though.