What would change socially if the earth was found to be flat tomorrow?

I’m amazed to discover that there are people out there that really believe the earth is flat. They are conspiracy theorists, and have all kinds of videos on YouTube.
If the Earth was flat, we’d need no time zones. We  would realize all those time zones and that International Date Line thing in the Pacific Ocean are all hoaxes too.
When the sun rises, it rises at the same time for all of us. It’s doing that now, right?
We’d probably all have to change our clocks and watches to British time. That would be weird but it would definitely affect what time you get up for work.
Of course, flat earth people believe the earth is flat, and it’s covered by a dome and there’s a big NASA and international coverup going on. I do fail to understand how the sun rises at different times, though.