But what is your email client using for notifications?
If it's using intermittent/timed fetch, that runs into the latency problem (taking longer to receive notifications). Push notifications exist to solve that problem.
If it's using IMAP's IDLE, MAPI's push, or JMAP's push, that's just another long-running HTTP or websocket connection.
And this protocol (along with the proprietary push notif aggregation services it is aiming to replace) exists to deduplicate those many long-running connections into a single connection out to some hardwired server that manages the many services/connections for it.
If it's using intermittent/timed fetch, that runs into the latency problem (taking longer to receive notifications). Push notifications exist to solve that problem.
If it's using IMAP's IDLE, MAPI's push, or JMAP's push, that's just another long-running HTTP or websocket connection.
And this protocol (along with the proprietary push notif aggregation services it is aiming to replace) exists to deduplicate those many long-running connections into a single connection out to some hardwired server that manages the many services/connections for it.