Or you could go the exact opposite, and do solar-local time everywhere.
We introduced time zones historically to make train travel easier. Now, we use navigation systems almost every time we travel long distances. It always shows me time of departure, time of arrival, and since they are non-round times and I can't be bothered to calculate the duration, it shows me that, too. If every city was in its own timezone, nothing would change. Just that duration would be slightly different than arrival-departure.
TV programming is basically dead, so you wouldn't have a problem with announcing when a show will run.
The only problem would be when scheduling online meetings. Frankly I rely on calendars for that, too. And often different places already have weird rules like meetings start 15 minutes later, or you should be there 5 minutes early.
The benefit of solar-local time is, I hope, that it will help people live more attuned to nature. You know at 12:00 the sun is at highest, that the daylight is symmetric around noon. People will be encouraged to make longer days in the summer and shorter days in the winter, maybe.