Yeah that wouldn’t work. Actually we should probably have more times with smaller offsets, the biggest problem with the time zones is always the edges where they’re way out of synch with the sun. 8 half hour time zones would fix that, though the TV networks would probably pee themselves.
Then when you visited different parts of the world, not only would you need to know that the seasons might be in different months of the year, you would also need to know that people worked different hours.
This might actually help with jet lag. If you go on a virtual reality ride where the movement of your seat is not correctly synched to the movement on the screen you will tend to get sick.
It could be that when we go somewhere else and are constantly told "It is 8am and we should be wide awake" but we just came from somewhere where it was 5am and we want to sleep in a bit more, that we suffer something similar.
If everywhere we go it is the same time then we will at least intellectually know when we should be tired and when we should be awake, and then only have to decide to gut it out when necessary.
Time zones are an anachronism. They were instituted when railroads were built. Even China only has 1 time zone.
With just 1 or 2 time zones, businesses would boom. Television programming would be more updated.