Parsing through progression shows a lot, it shows what phases people are suffering on mechanically, as you can see their DPS go down, and it also shows when people are more comfortable with mechanics as their DPS starts to go up on a fight by fight basis.
Seriously though what gets me is the people who are against parsers sound like they all have pretty bad groups. I don't use the parsing figures to call people out and say hey you, you suckwtf. If people are getting lazy with mechanics to inflate their own dps, then that's something the raid leader should be picking up on anyway as they are watching the fight. So you have both raid awareness for the mechanics side, and the parser for the DPS side. Your DPS need a bit of a knock on the head though if they actually get lazy with mechanics in order to pad their own DPS.
We use it to find where we are struggling, or where we are fine on, what parts need more practice, who needs a little more help than others, how can we change things up, could the tanks do more dps? Could the scholar get more DPS in to just push that phase before the next rage of bahamut? Is a certain mechanic making it hard for someone to keep up DPS (I.E earthshakers on monk in T13, so we use cover).
If you know the fights, you know where dps is going to suffer and you account for it (I.E blackmage t11 nerve gas), if there is no reason for someones dps to suffer and it still is, then you can quickly see that, and work on correcting it.
Ultimately, I like parsing through progression, not for the high numbers, but to see where things are going wrong. Mechanics I can see when people are screwing up, DPS and overheals are a little harder to keep an eye so the parser is just a great addition to help you see where issues are. Not to mention, its nice to watch the DPS go up every fight and actually have something nice to look at to know your group is getting better and better, till it goes on farm and then everyone just competes for the numbers for the fun of it.