> Got an example of a well-implemented natice app for email?

Mail.app isn't total shit. It's not great. But it doesn't fumble the basics, like Outlook for Mac, which thinks it's fine to take like 10s to show me my inbox.

Why does it seem to take so long to get & read one new email?

I can use get new mail or synchronize in Mail.app, but always spoiled by the instantaneous Gmail app notification. Often don’t have patience to wait for Mail.app for 2FA codes (just OCR or manually type from the Gmail notification mirrored on Mac).

Also should back up a bulk of ancient emails clogging the app, might be partially my fault.

Mail.app's search is completely and utterly broken in my experience on Macs and on iPhones.