Would you think web push notifications can replace email marketing?
I dont think so.When there are too many notifications, users might feel annoyed. They could choose to turn off the notifications. But, seldom of them might turn off the e-mail notifications as they're afraid of missing the important e-mails.
Email is still our "digital home". So for me email is still a place for transactional things and push notifications is a tool for customer nurturing.
The question is really broad. What kind of email marketing are you talking about?
No. Push notifications currently do not give the user the ability to fetch - some people get 20/30/40 etc to look through in the morning.
Push notifications are notoriously probably only 100 characters too - too short to get some points across.