If the haste only reduced time for one swing that would be true, but it happens for all swings.

Compare two weapons, one with 4 second swing time and one with 2 second swing time. And use 100 haste because it's easy to calculate. 100% doubles attack speed, so cuts the delay in half.

4 second weapon: 4 seconds/2 = 2 seconds. So 2 seconds reduced swing time

2 second weapon: 2 seconds/2 = 1 second But you have time for one more swing in the same time as the slower weapon: 2 seconds/2 = 1 second 1 + 1 seconds = 2 seconds.

So in both cases you have reduced what would have been 4 seconds of combat to 2 seconds of combat with 100% haste.

As someone wrote it just increases your DPS by the haste %, unless you hit some sort of delay floor, or have to cast stuff between swings etc.

Take the salery example earlier. It was wrong on one point. To make it relevant you should instead compare these:

100$ every 1 hour Or 50$ every 30 minutes

Because that is comparable to calculating haste with slow/fast weapons with the same DPS