I am all for getting rid of DST. It is arbitrary and far more trouble than it is worth. I am not sure how you could do away with timezones without a lot of confusion though, since they are based on and to account for the physical movements of the visible sun across the earth.
Use UTC, and adjust for local needs accordingly. If NYC stores open at 8:00 AM EST (UTC - 5:00), you would say, they open at 3:00. The advantage is that if a store owner in NYC calls a business associate in LA at 8:00 UTC, it is the same 8:00 for both even though there is still going to be a 3-hour time difference between them. Confusion over, "8:00 your time zone or mine?" is eliminated. In the case of the trip, time zones add confusion by distorting the time required for east/west travel if one goes purely by what the clocks say along the way.