Sea Hag is a powerful card, and one you should almost always open with. As far as the Cursing attacks go, it doesn’t get any more direct than this. No need to wait for the reshuffle for Familiar and Witch to start having an impact; no, just drop a Curse on top of your opponent’s deck and guarantee that they’ll draw a dead card next turn.
Does this mean that Sea Hag is superior to Witch? Probably not—the fact that you spend an Action doing nothing is a huge drawback. So certainly Witch is the better choice if you open $5/$2. But Sea Hag is strong enough that I would probably buy it with a $4/$3 instead of waiting for Witch.
The exception is with certain counters that directly benefit from having a Curse on top instead of in the discard (Lookout, Upgrade, Masquerade, and Native Village chief among them); even a +1 Action/+1 Card Action and a trasher in hand means the Sea Hag Curse goes away pretty quickly. In those situations, you should probably delay getting the Sea Hag and hope to jump to Witches instead. (Note that in multiplayer games, multiple Sea Hags make Lookout a far less desirable counter, since it’s quite likely your Curse on top will get discarded for another Curse.) If Witches aren’t available, consider delaying your Sea Hag purchase until later in the game; delayed Cursing attacks can be quite helpful because your opponent will typically have diluted his trashing ability with other cards, and possibly even Remodeled his trashers away.
Note that this does not apply to generalized early trashing: there is no reason not to open Sea Hag/Chapel, since your Cursing significantly slows down his ability to trash. This is a general principle applicable to all Cursing attacks, but especially Sea Hag, since it’s available from the very first turn and is therefore guaranteed to hit your opponent before he is able to trim his deck.
After the Curses are gone, you should almost never play Sea Hag, not unless you know your opponent has a good card on her deck. Either she’s been buying Victory cards, in which case you don’t want to discard one of them, or she’s buying good cards, in which case discarding will let him cycle her new purchases in slightly faster. Try to get rid of the Sea Hag as fast as possible, even trashing it to the Chapel if you can.
On a side note: along with Militia, Sea Hag is one of those massively-benefits-first-player cards; if you’re lucky enough to hit another player’s Sea Hag in the early game, that’s basically GG. The card could probably be reworded in a less variancy way, but its current form is probably an implicit concession to the limitations of the physical card size.
- Trash-for-benefit cards (e.g., Remodel, Bishop, Salvager, Apprentice)
- Council Room/Vault, since they’ll be drawing a dead card
- Throne Room / King’s Court (even though the benefit doesn’t strictly stack, all the Cursing attacks hurt much more when Throned or Kinged)
- Lookout, Upgrade, Masquerade
- Native Village
- The non-terminal +1 Action/+1 Card Actions, combined with trashing
- Reaction cards
- Other cursing attacks
- Your handsize-reducing attacks