This proposal focuses on timezones as names for hours and completely glosses over what the relationship is between timezones and days. Does Monday November 7th 2016 run from 00:00 UTC - 23:59 UTC? Do people in Sydney start work at 21:00 UTC on Sunday and come home at 17:00 UTC on Monday? Or do different places around the world have different times when they flip the calendar over? (in which case you've just recreated timezones by another name).

You don't get to get rid of the international dateline, either, because when every country chooses which two daylight-periods a week to use as their local weekend, even if everybody aligns them with their closest neighbors to the east and west right the way round the world, someone's going to find themselves having to make a choice between matching their western neighbor or their eastern one, because they disagree by a day.