The whole "it should be banned because it gimps tether/vertical recovery" argument isn't a legitimate argument by itself for banning a stage on the sole basis that it has disadvantages to certain kinds of characters' recoveries. Much for the same reason you can tell a player "don't play a character that can be CG'ed by DDD on walkoff stages/walls", don't pick tether characters on stages with bad recovery options for said characters. If a player wants to stick with one single character, they'd best be prepared and willing to accept the consequences of their character's pitfalls.
The "cave of death" and "loop" of skyworld is also mostly negatable due to their small size, and ability to have the problematic platforms destroyed. The cave on its own also it's very long nor is it tall, so many characters don't have issues removing their opponent from the cave. Add that the platforms are skinny enough to attack through, and that helps balance spacing issues caused by players separating themselves from each other between the platforms.
In my opinion, it could be close to bannable, if only there were anything else substantially wrong with it...but to me, it's just an awkward counterpick stage with advantages/disadvantages to certain characters, much like stages such as Melee's Brinstar and Mute City were (remember how much fun it was to recover as Falcon, Ness, Sheik, etc on Mute City?). Aside from the destructible ledges & platforms, it has a relatively neutral-style layout, with bottom/upper platforms, sided by two mid-platforms, with decent-ranged blast zones to the sides/ceiling/floor of the stage. Not too big, not to small.
And as much as I would personally love to see the stage gone, we owe each stage due process and evaluation; bias towards certain types of characters shouldn't play a big part in it.
Edit: Oh yeah, and as far as the "burden of proof" is concerned, the burden falls on the community and their members to first prove with due evaluation that the stage is Ban-WORTHY, not that the stage is worthy of becoming Un-Banned.
King Out