I think there's a general understanding in the business world that e-mail is for non-urgent stuff. It it's that important and you didn't make the effort to call, that's on you.
When I had a job that provided iPhones I routed all my personal e-mail through the Yahoo mail app and all my work e-mail through the Apple Mail App. Then I shut off notifications for the Apple Mail App so I only got notified about e-mail to my private account.
It depend on the job.
My job require a lot of data with urgent email for discussion. Some of these data in different file format not easily can be clarify on the phone or IM. Email to transfer data is the only way to help each other understand.