If timezones aren't good enough to display the time, what good are they? If Mexico is calling PST/PDT a different time than everyone else, shouldn't they be using new values instead?
The timezone names most countries use are not unique or entirely stable as time goes by. E.g., America and Australia disagree about what "Eastern Standard Time" means. That's why the Olson/Eggert database names zones for major cities, those are most stable and well known.