If you want to get even more radical, abolish standardized time entirely and just have everybody maintain a personal calendar that reflects the times they are awake, when they are busy, and when they're available. The proliferation of electronic devices gets us halfway there already, eg. iPhones have sleep/wake hours that tie into alarms and do-not-disturb, Google Calendar lets you set working hours, etc.

Way back in my pre-parent days, I used to wake up around noon, roll into work between 1-2 PM, work until around 10 PM, and then go to bed around 4:00 AM. There was briefly a proposal to give me and a few other late-rising coworkers rollback privileges to the Google Maps codebase, because between the Maps team in Zurich, the Maps team in Sydney, the Maps team in NYC, and a few night-owls in California, that would give them 24 hour coverage with significant overlap for handoffs. It went nowhere because we didn't work on Google Maps and some VP probably balked at having people not in their org with full owners privileges, but it's an interesting example of combining timezones + personal schedules to get better time coverage.