Okay, in response to an inquiry by Meno about 7 starter stages, I'll just post my full arguments/recommendations (personal) about them here.
As a brief aside, I'll attempt to demonstrate why 5 starter stages is inadequate. The main reason is that, for several characters, the commonly accepted starter stages are their best stages, sometimes overwhelmingly positive stages. The Ice Climbers make it obvious. Their best three stages in the entire game, including banned everywhere stages probably, are Final Destination, Smashville, and Yoshi's Island (Brawl). In a tournament with 5 stage striking, the Ice Climbers player always strikes Battlefield and whatever the 5th stage on the list is. If they win the first match (likely since it's on one of their best stages, essentially they counterpick on you match 1), they are set. They likely lose on your counterpick/use a secondary and hope for the best. Anyway, match three Dave's Stupid Rule prevents them from picking one of those three stages, and if you are smart your personal ban blocks a second. Still though, they just pick the third. This isn't one "neutral" and a counterpick per each side. The Ice Climbers player gets two counterpicks while the other player gets only one. The Ice Climbers are the most obvious case, but you also have lots of cases across the tier list of such things. Mr. Game & Watch sees his worst stages in Final Destination and Yoshi's Island (Brawl) so it's likely that any matchup in which one of the remaining three starter stages is against his favor will cause the 5 stage striking to produce unfair results for him. All sorts of chaingrabs work best on stages that are non-interactive, and if you're on the losing end of one of those matchups, this is going to be pretty unfair to you.
Seven itself isn't a magic number; there's no particular reason nine or eleven stages couldn't also work. However, seven is politically more obtainable, and it works very well itself. The goal is to produce a set of seven stages which produce the consistently most fair results when stage striking is applied to them; the most common sets are as follows
Battlefield
Final Destination
Yoshi's Island (Brawl)
Lylat Cruise
Smashville
Pokemon Stadium 1
Delfino Plaza or Halberd
Most people seem to lean toward the Halberd these days, but Delfino Plaza works pretty well too. Really, short of going through a ton of matchups and showing how this turns up fair, I can only call on my own experience and say that in most matchups (all matchups?) this produces a good stage.
The only real criticism I've seen is that some stages basically always get struck and should be removed which is kinda nonsense itself (the result is what matters, not the process), but regardless it isn't even true. I have seen every single stage on that list (including each of the possible 7th stages) played in the first match; I think it happens more once people get more used to the extra stages and are more comfortable playing on them (which, if they like winning, they will grow to be).
Some people like to make silly, absolutists statements such as "stages with X feature should not be starters" with no real justification. I would just remind them that they do NOT have to actually play on any one of the seven starters at random. If one of the starters is particularly bad for them, they can just strike it. Things are great and fair unless four of the starters are particularly bad for them in any given matchup, and I haven't found any matchups in which that's true. If the stage isn't bad for them but they're just complaining for personal distaste, they still could strike the stages they don't like anyway, and it might be worth reminding them that they had to be ready for that stage to be counterpicked on them anyway so they were already expected to be able to play on it.
A last note about stage striking is sequence. Most tournaments use a 1-1-1-1-1-1 order for stage striking (that is, the two sides take turns striking). This is really bad; my hands were a tiny bit sore from playing so much rock-paper-scissors after a long tournament with this. A better sequence is 1-2-2-1. Going second in general is an advantage (they could strike a stage you were going to strike, freeing you up to strike something else); this balances it out by making the "lateness" of the picks not strictly in the favor of either player (it's the 1st, 4th, and 5th picks versus the 2nd, 3rd, and 6th; the other order is 1st, 3rd, and 5th versus 2nd, 4th, and 6th).