Biggest downside I can think of, apart from the entire population groaning about making the switch, would be the confusion from reading literature from the before times. Oh, and all blood, sweat, and tears of all the devs who created timezone code going down the drain.
Mostly out of a necessity that fights tend to cross timezones and planes come and go from all over the world and they don't want to have to figure out everywhere what the local time is.
Really only passenger info screens convert to local time.
24:00 is "mid night". 02:30 is not less 'tonight' than 21:30, assuming no DST.
Because that only affects the comparatively small number of people awake respectively events happening at that time of day. If you move the calendar date change right into the middle of the waking hours of almost everybody else, things get quite a bit more annoying.
We might not specifically have time zones, but we'd have something that is equivalent.
We live on an approximately spherical world, its rotation is not tidal locked to its star, its rotational axis is not perpendicular to its orbital plane, we evolved to synchronize our biological rhythms including our sleep/wake cycle to local sunrise and sunset, we occupy a wide range of latitudes and longitudes, and we need to coordinate activities with people who are far away from us.
That puts a lower limit on the complexity of our time keeping system.
Fortunately they're not in charge.
They're still only a small minority a people, though. (In Germany for example ~5 % of people regularly work night shifts.)
Without timezones, in locations further away from the meridian a far larger number of people will suddenly be impacted. Having the calendar day change smack in the middle of waking hours of most people is rather annoying.
If engineers were in charge, there would be no time zones. Brits would get up at 08:00, Indians at 04:00, and Americans at 12:00/13:00/14:00 depending on location. Shops would set their opening hours relative to local sunrise. It's already the case that work-shifts span calendar days for many people, and that franchise locations have differing hours of business, and that fuckwits telephone you when you're trying to sleep.