Email Is Asynchronous
I don't understand where the problem is. Email is supposed to be completely asynchronous - you check it as often or as rarely as you like, without noticing delays (mostly) for the transfers. The longer you leave it, the more there'll be later. The inspired would use filters to help them manage large amounts of mail but this is only a disguise because you still have to check it in the end and it's a question of prioritisation. The uberkewl will implement his own push notification as by procmail/maildrop to chime a bell when new mail falls into the inbox as a hint that you might want to check mail now, and use email clients that actually follow standards to sort by threads.
Sixty mails a day? Ha! I'll have those if you'll manage my 350-400+/day spams, 300+/day listmail (including RSS feeds converted to mail messages)) and 30-40 new mails not counting uncaught spam and regular mailouts, thank you very much. And I'll take email over a phone call, any day. If you want to talk to me you can bloody well arrange it by email first. I HATE telephones! Just think of emails like letters, write formerly and nicely, and no txt spk pls.
It may be true that I sometimes feel anxious if I don't tend to my listmail too often, as I always like to catch up before the volume beckons me to blast the mail, but by and large I'm a happy email lover. I have always been. And I've never felt so compelled to check my mail as to give up other, often more enjoyable pursuits. You've just got to manage and pace yourself and use the tools available.
PS: there is no such thing as an empty inbox. I am, however, in negotiations to register the trademark. :-)