The apps that do push for Gmail are either from Google directly that they conveniently left support for themselves or from other providers that you have to grant access to your Gmail account so that every email would go through them for push--quite a few people don't want to have their email go through another company though, and those who are OK with it can use third party apps and companies that do that then.
Native email clients work the way Apples does where they don't go trogon their own servers to go through your email (again, as quite a few won't want that) and access your email from the provider directly supporting what the provider provides.
If Apple routed things through their own servers for email I'd likely be more upset about having to have my private email go through more servers and companies just for push notifications. And if I'm not upset by that then I can use a mail client that does that--which isn't a typical and expected or even necessarily desired feature or a normal email client.
i can kind of see why people say apple users hate choice. this seems like a perfect choice dilemma. in either case, i'm not a tech wizard and as i mentioned, i really don't care about why or what happened at all. i expect apple to figure it out because that's what a major billion dollar corporation should do for their customers.
again, you can't use 3rd party apps efficiently because they can't be the default mail app which means you have to leave your apple mail alive if you want to ever send mail through any of their other apps. which conveniently leaves apple pulling your mail twice and eating data. which is okay if you set it to manual, unless you ever need to send mail which will cause the mail app to pull e-mail
and to whoever said calendars haven't evolved. of course they have. i'll give you an example. there's an app called Tempo that automatically pulls yelp and/or contact information if it finds something in your e-mail. so if i'm having dinner with steve at cheesecake factory, it'll have steve's phone number and all of cheesecake factory's information within the appointment itself.