UTC or Zulu is great for data-logging and timestamping things, for later retrieval and reference. And also as a basis for figuring out when someone else in another time-zone is likely to be available, given the difference between UTC and their local time, as defined by the timezones. For scheduling any activity that involves people in different parts of the world it makes it unambigious when this activity is to take place. This is actually even more useful during the periods in spring or fall when the Daylight Saving changes go into or out of effect at different times in different places. So for example, deciding on a meeting at 15:00 in Oslo and 9 AM in Houston, by agreeing on this happening at 1400Z removes the ambiguity as to whether Daylight Saving is in effect or not at either of these places.
But as for a wall-clock time for general universal civil use, it is useless. Disregarding for the moment the general public's massive reluctance to this kind of change (compare with the less-than-great success changing to the metric system has been), the biggest problem is that each day will have one date in the morning and one in the afternoon. In timezone UTC-7 for example, such as found in the western US, this date changes happens at 1700 local time (or 5 PM), right in the middle of the afternoon. And since people mostly sleep during the night everywhere, there is still the need for others elsewhere in the world to be able to figure out when night and day occurs, in order to, for example, be able to schedule online meetings. The present-day tiimezone system, with all its warts and sillinesses, does a good job handling ths.
The original problem is that the twice-annual clock-changing caused by Daylight Saving is inconvenient, possibly minimally dangerous, and doesn't seem to serve much of any useful purpose. Any fix other than just leaving the clocks set to the same local time year will be worse than any of these, admittedly minor, problems that Daylight Saving has.