Consider this. Suppose I want to phone someone who lives in Japan and I live in the UK. Japan is +9 hours ahead of UK local time (GMT). Therefore I know if I phone slightly before lunch then I'll be phoning them in the evening.
Now suppose we all had the same time. If I phoned them just before lunch, which would mean shortly before 12:00 in the UK then I'd have to try and figure out what Japan would be doing at that time. Would 12:00 in Japan be early morning, late at night, would they be eating a meal, would they be at work? Now I have to remember where in the day different times are for different counties. However, with timezones all I need to remember is a numerical value and I can easily figure out where Japan is in the progression of a day (i.e morning, evening, night).
You need to remember the exact same bits of information in both cases, so I don't see the problem. In one case you remember it as "time difference" ("now is 12:00 +9 there"), in the other case you remember it as earlyness/lateness compared to you ("12:00 here is LIKE 12:00 +9 there").
So that would need the same exact effort.
The man benefit would be for the "let's meet at the same time online" etc coordination stuff -- where's its brain-dead easy when everybody has the same time.
Ok, but I know a lot of people who are available at work at times which do not match the "usual" work hours. Also shops have no universal opening times, some open at 7, some at 10, so you always have to check if the other side is available before calling (or just try).
I guess calling would also be easier if the used system can show if the other side is available like Skype or even better when she is available.
Now suppose we all had the same time. If I phoned them just before lunch, which would mean shortly before 12:00 in the UK then I'd have to try and figure out what Japan would be doing at that time. Would 12:00 in Japan be early morning, late at night, would they be eating a meal, would they be at work? Now I have to remember where in the day different times are for different counties. However, with timezones all I need to remember is a numerical value and I can easily figure out where Japan is in the progression of a day (i.e morning, evening, night).