I hope that we can stop trying to sync noon to the local sun at some point. I think it made sense when communicating over distances was hard and rare. In that case giving local time some meaning (ex: "People tend to wake up around 8") had some value. However now that communicating with people around the word is commonplace I think that benefit is outweighed by the value of knowing what time people are talking about. Because if you try to schedule something before I want to wake up it is incredibly obvious to me. However if we mess up the timezone math by and hour no one will notice unless they think to explicitly check.

The only real downside I see is that if the day number changes during your "day" it could be confusing. However I think we will quickly learn to deal with it (overnight shifts have been a thing forever and doctors seem to manage). Plus we already have a weaker form of this when we are talking about late-night activities so I think we will figure it out.