You can edge slip on every platform, the thing is that (you'll understand if you watch the entirety of the video I linked) if the opponent hits the ground DURING their edge slip animation, they go into the 'missed tech' state.
eg if MK's edge slip animation is a total of 27 frames and he hits the ground 27 frames after sliding off the platform (or he hits it in less than 27 frames) then he'll go into the missed tech state. If he takes longer than 27 frames to hit the ground, he's not forced to go into the missed tech state (ie he can airdodge, do a move, jump before hitting the ground) but if he doesn't do any of these before hitting the ground he'll still go into his missed tech state.
This applies to every character.
Now...whether or not the opponent will hit the ground during their edge slip depends on
-Height of platform
-Character's edge slip animation length
-Character's natural fall speed (ie not fastfall speed)
So on stages with higher platforms (eg Smashville, PS1, Delfino), fewer characters are guaranteed to hit the ground than on BF.
On stages with lower platforms (I think Lylat is the only one?...Also some transformations of PS1/PS2/Delfino) more characters are guaranteed to hit the ground than on BF.