Edit: Give me an example of a low tier who suddenly does better on awful stages that doesn't involve walkoffs. The only one I can think of is MAYBE Link/Young Link because they can can't cancel their projectiles, meaning their spam isn't crippled by having to dance around on a stage. However they have laggy *** aerials that mean they're crippled if they go air to air for long periods of time.
First off, you just answered your own question by saying "that doesn't involve walkoffs". That means that lower tier characters can suddenly have an advantage on a certain type of stage, showing that there are stage qualities that can switch things around.
Second, you're saying "low tiers". I'm not saying low tiers. I'm saying "not top tiers".
Top
Fox 9.88
Marth 9.85
Sheik 9.69
Falco 9.15
High
Peach 8.35
Captain Falcon 8.00
Jigglypuff 8.00
Ice Climbers 7.88
Middle
Samus 6.77
Dr. Mario 6.23
Ganondorf 6.04
Luigi 5.81
Donkey Kong 5.38
Mario 5.34
Low
Link 4.69
Pikachu 4.31
Young Link 4.15
Roy 3.60
Zelda 3.04
Game and Watch 3.00
Bottom
Ness 2.50
Yoshi 2.46
Bowser 2.17
Mewtwo 1.77
Kirby 1.50
Pichu 1.15
But hey, you said low tier, so I'll just use low and bottom. I'm sure you can go through and see Peach, Jiggs, Samus, and other characters that play differently than "move and fall really fast using a lot of aerials"that are unable to play on stages that naturally benefit them. I'll leave that part up to you.
Anyway, low tiers.
Low tiers do not become good because they're playing on Brinstar Depths or Big Blue.
I'm assuming any stages are fair game, not just the ones from the "old list" based on this quote.
Icicle Mountain
Pikachu and Pichu, with their high mobility, projectiles, and vertical KO power can do well here. In many matchups, these stages would be better suited for the electric rodents than, say, Battlefield or DL64. While Falco could dominate here easily (his shine KO is pretty beastly) and Fox is no slouch, characters like Marth, Sheik, or Captain Falcon are going to have a more difficult time in these matchups than they would otherwise.
Yoshi's double jump to nair is also incredibly effective on this stage. Due to the whole "no knockback lol I'm Yoshi" factor, Yoshi is safer than most when manuevering against the stage's vertical scrolling. Yoshi's neutral b is also no longer useless, as it puts the opponent in a pretty bad position during the fast scrolling areas.
Termina Bay
I wish I could talk about DK, but I'll have to settle for Link's amazing up+b instant KO here. He's not alone in holding a quick KO on this stage, but the layout makes his bad recovery less of an issue, he has quick gimping abilities against the entire cast, his shield stops any sort of projectile spamming from across platforms, and due to his grab range and projectiles he is one of the few characters that can approach someone camping the edge in their shield safely. Someone camping hoping for a quick KO can be pushed off the ledge safely by Link, or can simply be grabbed. Any opening this creates leads to standard combos against Link rather than the quick death the opponent was hoping for, while any mistake on the opponent's part leads to a pretty fast death. Link's up+b when an opponent is on the ledge is also pretty beastly, as it will hit them (and kill them in many scenarios) regardless of their action.
Mewtwo's over-b glitch is pretty amazing here as well, as anyone approaching from the top platform can be dropped through. It doesn't combo and isn't guaranteed, but the option helps.
Flatzone
Hello, Roy.
I'm bored with this, but you get the idea.