Sadly, I could never see our clients accepting any business day where we are not available during regular business hours.
I had an interesting call with a doctor client recently. "I didn't notice a number on your website." "That's correct." "So how am I supposed to get in touch with you?" "I recommend email." "But you only respond to email a day later." "That's correct." "Shouldn't you make yourself more available to your customers?" "With respect, doctor, I'm exactly as available as I wish to be."
You would think she'd be mad after a conversation including that, but she actually left happy, because I was able to fix her problem.
Of course, you could also just hire a remote assistant to field phone calls for you if you wanted.
I firmly believe we'll see more people move to a consulting model where they work far fewer hours, are more productive and make as much or more money as before.