It really baffles me how bad the GMail app on iOS is. I was hoping that Inbox would be a step up, but like you said, I don't want my email managed that way.
I have a work Google apps account and a vanilla Gmail account and it is frusturating not having a unified inbox. And I keep getting "Network errors" with it (on two devices that I tried).
I recently dumped the GMail app for Outlook on iOS and it has just been phenomenal. I wish the search was a little better and I could see my GMail labels, but for now, it looks like I won't be going back.