There's probably some research somewhere estimating the cost to business (or loss of revenue) from mistakes in doing timezone conversions. In the simplest case, if you have a business call with someone halfway around the world, and one of you has recently gone into or out of daylight savings time, then there's a good chance the call will not happen when it should. Or perhaps you were supposed to be watching a political debate online at a given time so you could provide instant advice and feedback to advisors present in the debate, but you missed it because you didn't realize they had left DST a week before your location does.
I could go on and on with examples of the human cost to keeping the current system.
So let me say this: _coming up with the ideal system is not hard_. But how will you transition the world from its current state to this ideal state? Consider that the metric system (or SI), which is much better than the US system of measures, has still not been adopted in the US. Why? Because the problem of transitioning between systems is called politics.
But if you do much international travel, at some point you will encounter the problem where your various calendars, clocks, and other tools don't do the right thing (perhaps they get incorrect location information, or any number of other problems occur).
Then you have dis-information. If you don't realize it, then you will suffer by missing something important or wasting your time.
The tools are far from infallible now, and there's really no hope that they will ever work correctly.