This is a biased article. I would not let another company handle authentication or notifications for my apps. Payments, yes.
> notifications for my apps What kind of notifications are we talking about where you can get away with self-hosting? AFAIK, Push Notifications on smartphones have to go through Google and Apple's servers. Maybe if you're doing email notifications?
For email though, not sure, that's a completely different topic. It comes with many headaches, using a service like SendGrid or Mailchimp seems like a good idea, and if you really want to roll our own mail servers down the line you can still do that.