I think status is still important, depending upon the airline.
It is easier to get upgrades with status, one way or another. Even on cheap fares.
You are less likely to wait in long lines.
You can use the elite security line when there is one.
It depends upon the airline of course.
The bottom tier on NW has proven valuable to me because I get a lot of domestic USA upgrades free. But the bottom tier on UA, Premier, doesn't seem to mean much on UA.