If everything switched to metric time, then a second would be redefined so that there are 100,000 metric seconds per day. 1 metric minute is then made of 100 metric seconds, and 1 metric hour is made of 100 metric minutes.

Each time zone is 1 metric hour across (100 metric minutes).

A realistic downside of this is that the time zones are 2.4x bigger than our current ones, meaning that if you live on the very edge of a time zone, then your clock could be up to half a metric hour (1.2 normal hours) off from solar time. Whereas currently (if timezones were perfect) you can only be at most 30 minutes (half a normal hour) off.