Battle Bond: Forme change, banned because of the BST rule, only usable on Greninja. It was legal for a short time back then and I used it a bit. Normal Greninja without an ability isn't great, and killing something as Greninja means it's a 2v1/1v1. The extra stats are too late to be worth it imo, unlike other abilities that can be in effect the whole game. The Water Shuriken change barely affects the game. If Ash Greninja was selectable from the start, this ability would be useless unless you get Water Shuriken regularly.
Cheek Pouch: Heals 1/3 HP when eating a berry. All the 50% HP proc berries are banned under the healing rule too, so you have to go with pinch berries/Kee/Maranga/Leppa. If all heals were allowed, you could combo with a 50% pinch berry and heal 83% at 25% HP or less, or Sitrus for 58% at 50% or less. Not bad, though there's the risk of being in kill range and just outside of heal range with the pinch berries. Steel types will probably lose their HP slower on average. Unnerve/Magician can counter I guess.
Cursed Body: 30% chance to force Disable/3 turns of Struggle on any hit is crazy and pretty reliable.
Desolate Land: Infinite sun that blocks water moves. Not many good sun abilities to combo with. Flower Gift is Cherrim locked, Chlorophyll's Speed doesn't help too much, Comatose is usually better than Leaf Guard, and Solar Power's passive damage isn't worth it. (EDIT: Harvest is a good one I forgot about.) Water isn't a major weakness to avoid for the meta except Camerupt. Has some competition with a slower Primordial Sea or Delta Stream/Air Lock.
Dry Skin: Passive 1/8 healing in rain, heals 1/4 from water moves, but takes 1.25x damage from Fire and passive 1/8 damage in sun. Really great with Primordial Sea, but rain is limited to 5/8 turns via Drizzle or RNG otherwise. With Leftovers, you can really last a while off of healing and turns where nothing happens. Aside from the rain healing, I'd say Storm Drain is a better water immunity because it attracts moves. Water Absorb doesn't have the fire weaknesses.
Fluffy: Half damage against contact moves, but 2x Fire damage. Fur Coat is better in most cases aside from the rare contact special move.
Fur Coat: 2x defense, no drawbacks. It's not Magic Bounce level, but it's a big boost that's active all the time. Mega Steelix gets 1000+ Defense. Can combo with Kee Berry for even more defense. Steel types/the meta mons have solid physical stats in general, so this will defend against the higher attack stat most of the time.
Grassy Surge: Passive 1/16 healing terrain, boosts Grass moves. 4 healing turns from the start isn't that much, could be annoying if you get one strong hit on Turn 1 and whiff all your next moves. Also halves some Ground move powers, more occasional help for steels. Grassy Seed and Grass Pelt can boost Defense but aren't optimal. Grassy Terrain is callable on its own, so people have probably played in its effects at least once.
Huge Power: 2x Attack, no drawbacks. Like Fur Coat, it's active all the time and provides a major boost. You can combine this with a Choice Band for really high Attack. Super effective and STAB moves get really dangerous, and even chip damage like Nuzzle or Struggle can do more than expected.
Ice Body: Passive 1/16 healing + hail immunity. Not very reliable to use, since Snow Warning only happens at the start of the match (exception: Mega Abomasnow) and getting Hail is otherwise RNG. Overcoat/Magic Guard can cover the hail immunity and more. Still, with Icy Rock the Hail lasts 8 turns and with Leftovers
Iron Barbs: 1/8 damage against contact moves. With Rocky Helmet, this combines to make a brutal 29% on each hit. Alone it's not as bad, but the passive damage is noticeable, especially against tanky steels. Magic Guard is a hard counter.
Moody: +2 and -1 to a random stat per turn. Adds more RNG to the RNG metagame. After enough turns, there are so many boosts that regular mons just can't keep up. Unaware could neutralize it.
Parental Bond: Adds an extra 25% damage hit to moves. Unlike the normal metagame, you can't take full advantage and choose to use a set damage move or whatever. Best used on glass cannons/high attack mons. I don't think it's game breaking. It was legal for a short time through a Kangaskhan loophole, and I don't recall it being that effective.
Poison Heal: Heals 1/8 HP per turn when poisoned. With Toxic Orb, this is better than most passive healing (Leftovers) and protects you from other status.This ability was the one that showed me how strong consistent passive healing can really be, survivability increases a lot. Fortunately, steels can't take advantage of this strat because of their immunity.
Power Construct: Turns Zygarde into 100% which is banned under BST rule. If Zygarde 100% was legal then I imagine you could just select it in the first place with an actual ability. If there was a scenario like Greninja where you had to Power Construct to activate it, I think having an ability would still be worth more than a mid battle HP boost.
Pressure: For all the pressure on it, this ability doesn't even affect Metronome because it targets the user. If it worked like most people expected, it would be all over the meta. You can kind of get the same effect with Truant to halve your own turns.
Primordial Sea: Infinite rain, immunity to fire. This helps steels, Scizor especially. It's like Flash Fire, but for the whole field so you can run another ability or just appreciate the extra immunity in general. Rain Dish and Dry Skin are good passive healing abilities to combo with. Swift Swim and Hydration are not that great. Can be stopped by Delta Stream/Air Lock or a slower Desolate Land.
Protean: On the surface, it's free STAB on every move. The power isn't bad (should be used on an attacker/mixed attacker), but the type change is very noticeable in terms of defense and feels like Color Change. Losing Steel resistances can make mons a lot less consistent and really lowers survivability. Worse than I expected.
Pure Power: 2x attack. See Huge Power.
Rain Dish: Passive 1/16 healing in rain. Can combo with Primordial Sea or Drizzle, as well as Leftovers. Dry Skin's 1/8 healing is better though.
Rough Skin: See Iron Barbs.
Sand Stream: Passive damage, though the meta is full of steels that it doesn't affect. Sand Rush isn't viable, Sand Force is reliant on Metronome getting specific moves to boost, and I guess Sand Veil can be annoying. Mega Tyranitar can get 2 Sand Streams, though banned under the BST rule. Rock types are rare and probably won't be able to take advantage of the SpD boost.
Schooling: Banned because of the former BST rule that blocked Wishiwashi School, only usable on Wishiwashi. Since you can use School forme alone, this ability doesn't provide anything and just makes Wishiwashi weaker now. If Schooling was the only way to use Wishiwashi School, it'd at least be usable from the start but wouldn't have an endgame.
Snow Warning: 5 turns of hail/4 turns of passive 1/16 damage. Ice types are rare so this will affect most mons. Can combine with the Icy Rock for 8 turns of Hail. Snow Cloak can be annoying, Ice Body can heal, and Slush Rush is meh. Mega Abomasnow can get 2 Snow Warnings.
Stamina: +1 Defense when hit. Similarly to Moody or Fur Coat, this ability lets you tank any physical move after a few turns. Easy for steels to get going thanks to their resistances and initial bulk.
Volt Absorb: Heals 25% when hit by an Electric move. I prefer Lightningrod as an Electric immunity since it draws moves in. The healing isn't consistent either and relies on Metronome, unlike some of the passive healing that you can get for a few turns/every turn.
Water Absorb: Heals 25% when hit by a Water move. Same opinion as Volt Absorb, there's Storm Drain for Water immunity that draws moves in. The healing can come in clutch, but it's not reliable.
Wonder Guard: Very broken, relies on RNG to hit. Still vulnerable to status moves, but there's a good chance you won't inflict any direct damage against a Wonder Guard user. Loses to Mold Breaker.
Sturdy + Shedinja: For the most part you're invincible, but still vulnerable to some status moves. Also loses when forced to use/gets hit by Struggle, so you have to hope Metronome lets you hit some good physical moves to get past those steels. You can actually get this combo via Power of Alchemy sacrifice though I wouldn't recommend it.
Harvest + Rowap/Jaboca: 1/8 HP passive damage berries. Harvest procs often enough even without sun. I've tried some Pickup variants, but it all comes down to RNG. The damage is helpful but not totally reliable.