To send from a different 'From' in Mail.app, first you need to connect your iPhone to additional email accounts (Settings->Mail). Then these addresses will show up in your 'From' drop down.
But then you end up with multiple inboxes in your Mail.app. Which is messy, fills up storage, and hurts my brain -- since I never need to check my other inboxes (because all my email addresses forward to the same Gmail account).
With the Gmail iPhone app, I just need to prove once (in gmail.com) that I have access to whatever 'From' addresss I want. Then I can select them in the Gmail app.
Note: I admit that the viewport issues discussed in the blog post are indeed an annoyance that I hope Google fixes soon. But I prefer Gmail app to Mail.app nonetheless.