For me it's because I've come to rely on the Gmail tabs (primary/social/promotions/updates), which the built-in Mail app just ignored. I could probably duplicate the effort with folders (though I use those also, in parallel to the tabs), but I just started using the Gmail app instead which handled it all fine.

A year or so ago Google removed the Exchange support necessary to do push via Apple's mail app (well, it's complicated: if you set up GMail via Exchange on the mail app prior to that point in time your device is grandfathered. Otherwise you've got to use the GMail app).

Not the OP, but I noticed the same and in my case the reason it's simple: I have all my email/attachments since 2004/2005 in gmail. I use full archive search way more often than I care to admit.

I love how gmail works/syncs across all platforms (my iPad on iOS, two Android devices, PC laptop and Mac desktop) and doesn't limit me to the Mac/iOS platform.

Unfortunately search barely works for me on Mail. That is a big one. Also, in the mornings before work I like clean out my mail but I don't have access to my Gmail primary tab so I tend to tons of unnecessary email. Labeling also doesn't work.

I would also recommend Mailbox for managing Gmail. It is one of my favorite apps I have ever used.

I cant seem to get push notifications to work with the OS app, is there a way around this?

Push notifications, I believe, don't happen in Mail.app?