As to why this concept matters, you really only have to look at what they add, competitively. Let's say we work backwards (everything is banned, stages are unbanned one by one). When I add FD, I have a game where, when I main a character, I have to learn 38 matchups on one stage.
Now we throw Battlefield into the mix. All of a sudden, I still have those 38 matchups, but some of them play drastically differently on battlefield than they do on Final Destination!
Now we really throw everyone for a loop and add Norfair to the mix. Now I still have these 38 matchups, but now I need to not only learn how to play them on Battlefield, Final Destination, and Norfair, but I also have to learn how to play on Norfair at all! Once I've done that, I find that trapping my opponent with the lava if he is inexperienced becomes a very potent strategy, forcing him to learn how to play the stage or to die (imagine it, if you will, like a character matchup-if I run into the ICs and never have played against them before, I won't know that one grab = death until I've already suffered it. If I run into norfair without ever having seen it before, I won't know how to deal with the lava). I also have to, in turn, find ways around this strategy.
Now we add PS2 to the mix. Now I still have the 38 MUs, but not only do I have to know them on these 4 stages, have to know how to play on Norfair, but now I also need to know how to deal with PS2's transformations, know how to take advantage of the changes to the best of my ability, and how to get around things like MK's uair on the air segment. This is a RIDICULOUS amount of things you have to learn to play the game competitively at a high level. In other words: it adds to the competitive merit of the game.
So in short, by adding more stages, we are almost always making the game more competitive by giving it a longer learning curve. If you only have to learn 38 matchups on FD... oh well. If you have to learn 38 matchups on FD, Battlefield, Norfair, RC, Halberd... It's a lot to learn, and a lot more chance for someone to shine who is good at many facets of the game, instead of just one particular part.
The only cases where this doesn't apply are when the stage itself is drastically anticompetitive. To continue the pattern above:
Now we add Warioware. I have 38 matchups and 5 stages, but now I also have to learn how to deal with drastically unfair randomness. I am the best in the country, and some random scrub beats me on this stage about half the time because whenever I win a minigame I go giant or get nothing, and whenever he wins, he gets a star.
This is anticompetitive. The stage gives far less in than it gives back. I don't think I have to explain it that much.
In the cases of stages with choke points such as PTAD, or stages where a certain character is just way too good (Brinstar, RC), this is the question that needs to be asked. Through thorough testing. But seeing as stages are, by default, unbanned, it's up to the people who believe a stage are wrong to conclusively show that it is broken, and that it is a bad stage to have legal because it lowers the competitiveness of the game .
Banning almost any stage out of hand that doesn't fit one of the criteria I posted above is scrubby. In fact, it's pretty much exactly scrub logic-"I don't like this, let's ban it" (ignoring for the moment that usually, scrubs hate FD/BF/SV instead of RC/Norfair/GG/PTAD). Such decisions can only really be made effectively after one of two things happens:
1. The stage has been thoroughly and exhaustively tested. Remember how long people waited on the button to put Garchomp into Uber tier? Or how long it's taking to ban metaknight? Or how hard banning Hilde was/is?
Is PTAD really that bad for competitive brawl, or have we just looked at it, shouted, "OMG DANGEROUS MAP BAN BAN BAN" like an idiot scrub would say when looking at something like DDD's CG or G&W/Pit's planking? I'm going to argue the latter. It was only ever allowed in some parts of the midwest, and whenever a thread was made about the stage, the complaints were coming from... Well, I'll give you a hint-it wasn't people in the midwest who had actually used the thing in their tournaments-it was people from the more conservative regions, bawwing over a stage that they had probably never played on in their lives.
2. The brokenness can be logically explained. There isn't really any need to look at a stage like Spear Pillar, because it has criteria that automatically disqualify it, such as the cave of life and the large circle. Same with stages like Warioware, where it's obviously too random for any kind of competitive play. However, you can only really apply this to stages where it's brutally obvious-if someone challenges your proposal with any credible argument, then you should either go to 1. or revise your argument completely. See, for example, the thread about Mario Circuit in the SWF stage forums.