You still inherently have to keep track of time of day in the other regions though. Consider trying to schedule a meeting between a group of people across India, Ireland, and East Coast US under a single time system. Instead of knowing that 9AM EST is 2PM in Ireland and ~6:30PM in India. I now have to look up the standard business hours in each location.

Also that system will probably devolve into defacto timezones without actual definitions where business in nearby areas decide on what constitutes reasonable hours based on businesses around them and the relative solar time but instead of reasonably crisp boundaries like you have today defined on a map it'll be a slow bleed and interspersing between multiple sets of '9-5' hours.