So, Catapult. I think this card is significantly better than its current placement. I'll try to explain why.
Disclaimer: I've only played a few games with Catapult, and this card is especially hard to grok. I'm not surprised that it has a high deviation.
If your gut reaction is that Catapult is a weak card, please recognize that it is a thinner + attack card. The only other thinner + attack cards (Ambassador + Mercenary) happen to be some of the strongest cards in the game. Catapult may not be as powerful of those cards, but it is in elite company. The thinner + attack cards are deceptively powerful, because they improve your deck while making it difficult for your opponent to improve their deck. To a new Dominion player, playing Ambassador might feel like it isn't accomplishing much: you often end with two bad cards in hand and nothing to buy. Despite this subjective feeling, Ambassador is one of the most potent cards in all of Dominion. Urchin/Mercenary is similar. It doesn't feel powerful to buy and play weak cantrips multiple turns in a row. It doesn't even feel great to play a Mercenary and end up with $4 or something. Yet, pursuing Mercenary is correct on most boards. These thinner + attack cards don't feel as powerful as they are. Catapult is no exception.
I'm going to divide all kingdoms (involving Catapult) into three types: those where Catapult is the only Estate/Curse trasher, those with another single-target Estate/Curse trasher, and those with an elite multi-card trasher.
Catapult as only Estate/Curse trasher
Catapult can give out Curses. If player A goes for Catapult and player B doesn't, player B will have Curses in their deck that they can't trash. How fast can Catapult reliably give out Curses? Consider a baseline strategy of only using the base cards and the Catapult/Rocks pile. Player A buys Catapult on turns 1-5 and Rocks on turns 6-10 (unless they get an unlucky $3 hand). Ideally, Player A trashes Estates on turn 3 & 4 (sometimes Catapults collide, or miss the shuffle, or miss Estates). Starting on turn 5, Catapult collisions will be more common. The first two times Catapults collide, player A trashes Catapult with Catapult and gives out a Curse. By turn 7, the Catapult player will have given out at least one Curse. This is on par with Witch BM with a 3/4 opening. Available starting with turn 8, Rocks become a top trash priority, which junk, reduce handsize, and provide +$3 for player A. Indeed, almost every turn from turn 8 onward will either junk (trashing a colliding Catapult), reduce handsize (trashing a Copper), or both (trashing Rocks or Silver). Trashing all of the Rocks and two Catapults will give out seven Curses (realistic by turn 15). That is an oppressive amount of junk. Plus, player B will often be subject to handsize attacks. Player B won't be buying many Provinces. Player A, meanwhile, is steadily improving his economy with the Silver from Rock gains and trashes (10 total). Player A can either rush Duchies (two other piles will easily empty) or buy a few Golds and go for Provinces.
And this is just a baseline. There are other kingdom cards that can help the Catapult player (villages, card draw, sifting, gainers). Catapult is going to be the dominant strategy on most of these boards. Exceptions include especially potent defensive cards (e.g. Watchtower), powerful junkers that can give out Curses faster (e.g. Young Witch w weak bane), and fast strategies that aren't crippled by attacks (e.g. Rebuild).
Catapult with another Estate/Curse trasher
Suppose the kingdom includes another card that can trash Estates and Curses, like: Ratcatcher, Raze, Lookout, Forager, Amulet, Hermit, Salvager, Junk Dealer, etc... Might it be best to avoid Catapult? I think not. In most cases, opening Catapult + other trasher (or Silver to get a $5 trasher) will be dominant. Why? Catapult isn't especially good at trashing Estates and Curses, but it is very strong when it trashes Copper. Having one of the aforementioned trashers frees up Catapult to trash Coppers almost exclusively. The handsize attack will really slow down your opponent. Have you ever tried to ignore Urchin in favor of a non-elite trasher? It's really painful to discard down to three when you're trying to trash. Either you give up on trashing, or you spend your turn doing nothing but trashing a single card. Playing against Catapult can be similar. Buying a Catapult of your own won't solve the problem, but now you and your opponent will suffer together.
Exceptions exist, of course. If you open with a power $5 trasher like Junk Dealer or Sentry, you can probably ignore Catapult. Masquerade draws, which means it combines poorly with other trashers and it can mitigate Catapult's attack. With Masquerade, you still might want to pick up a Catapult later on if you can orchestrate a handsize attack followed by Masquerade. I have no idea how Jack of all Trades and Catapult get along. Jack can counter the Catapult attack, but Jack loves Copper trashing and Catapult likes Silver gaining, so maybe they are a potent combination. Are there Copper-trashers that outclass Catapult in these situations? I'm not sure. Spice Merchant and Counterfeit stand a chance. It will probably depend on the rest of the kingdom.
Catapult with an elite trasher
Suppose the kingdom includes a card or event that can trash multiple cards in one turn: Donate, Chapel, Ambassador, Steward, Remake, etc... Here, Catapult is not a very strong opening. Even if the Catapult player gets lucky and hits the Chapel player with a handsize attack with their Chapel in hand, they can still trash two cards of their choice, while the Catapult player needs to trash Copper and not Estates to keep the attack going. It's a losing battle. Catapult is even worse against the two-card trashers; the discard attack is almost useless. Still, Catapult isn't a dead card on these boards. It might be worth picking up a Catapult after the thinning phase for payload, especially if there is an easy way to gain $3+ cards.
Catapult is a strong card in almost every kingdom. It is usually game-warping if it's the only card that can trash Curses. It is a strong Copper trasher in combination with an Estate/Curse trasher. And in the rare kingdoms where it is too slow to trash, it can still be valuable as payload. Similar to Ambassador and Urchin, it might not be pleasant to play with or against Catapult, but that is a consequence of its strength, not its weakness.