Just about every single one of them by the logic you proposed. Does Hyrule Temple have random elements with an overwhelming influence on play ? No. Is it overly advantageous for certain characters ? We have no clue because we've never seriously played there, and you'd have to consider which part of the terrain they're playing on. Already Hyrule Temple escapes your two criterias for determining how stages should be allowed, even though it promotes situations where neither players wants to approach (like all stages that have big dividers) and nobody seriously wants to allow that stage in a tournament. Onett could be another example, as could Fourside. Even if we had clauses that exclude stages with walkoffs and major dividing walls, we still have Hyrule Castle, Castle Siege or Rumble Falls in PM, Kongo Falls and Rainbow Cruise in Melee (Pokémon Stadium sets a precedent for temporary banned features) that are systematically banned while not being covered by our four criterias.
Player's opinion is also something to consider. While people may accept to play on Metal Cavern or Dracula's Castle, the more alien the stage is, the greater the negative reaction. Ultimately most tournaments are held for the players, so their enjoyment is paramount to success and should absolutely be considered when creating a stagelist. Camping is not enjoyed by a great number of players and spectators, and thus we can justify excluding stages that promote it in excess.
On another topic Smash Down South 2 recently ran a stagelist with Metal Cavern on it and so we've got some video footage of matches there :
http://youtu.be/BStYnWzk-Fg?t=8m (Kirby vs Ike)
http://youtu.be/aYfK_JQnn2Q?t=7m50s (Ike vs Snake)
It is a well known fact that Hyrule Temple is banned because of it's massive size, which gives far too great an advantage to characters who are fast and can run out clocks and/or camp, as well as because the massive size gives a huge advantage to characters which kill off the top, as killing off the sides is extremely difficult on a stage so horizontally wide. See:
http://supersmashbros.wikia.com/wiki/Hyrule:_Temple#Competition
You do, however, bring up a good point, and Hyrule Temple is a good example of it. Another reason it is banned is because of the "cave of life" at the bottom, where a character can live for ludicrous amounts of time given the right amount of teching ability. This does not cover either of my two criteria. So, I'd be willing to amend my list with another reason:
3. The stage greatly encourages play styles which slow down and/or change the general nature of the game.
Onett does not pass my first two, as walls allow for certain characters to have infinites or extreme lock downs (large advantage), and the cars present a very large chance element, in that even if you don't get hit, given the very limited space available on the stage, being forced to move away greatly limits your options, far more than, say, a giant laser on a flat stage. Walk offs in general are relevant to my second rule, as any character that kills largely by gimps or spikes is SOL, and characters with chain grabs have a possible super early kill. It also fails the new third, in that the walls are going to cause some serious teching matches, and the walk offs encourage blast zone camping.
Fourside fails #2 because it gives a massive advantage to characters that can wall jump. Recovering becomes extremely easy in the middle pits for those who can. The platforms are also extremely small, which gives a large advantage to aggro and tech chasing specializing characters. You could also make an argument for #3, as teching the middle pillar could be annoying, but I could see that one going either way.
Castle Seige fails #1 because inopurtune transformations with little warning can give characters a free out from tech chases and combos, as well as cause failed recoveries.
Rumble falls fails # 2 because it gives a huge advantage to characters which cover vertical distance quickly, as characters who do not will have to spend much of their time just trying to not die off the bottom. It fails #3 for that exact reason.
Kongo Jungle fails #3 because of the rock on the far right, which encourages camping/stalling. By extension, certain characters can take huge advantage of that over others, so it fails #2.
Rainbow Cruise is a similar issue to rumble falls, in that it forces characters to use their mobility resources on merely surviving, giving a large advantage to those characters with mobility resources to spare, thus failing #2. It could also be argued to fail #3 due to runnaway stalling, though that is more minor.