Context is king. If there’s vital/time-dependent correspondence you’re waiting on, notifications can matter. But email in 2024 is pretty darn transactional, in which case a daily check is enough for most. Notifications for something suggest that I need to drop what I’m doing and attend to whatever arrived. That just doesn’t apply for service provider marketing, purchase receipts, etc.
And then the opsec angle comes into play: https://www.axios.com/2023/12/06/apple-google-requests-push-notification-data
The only objectionable hurdles are the insurmountable ones