
I don't think this card is quite so limiting as all that.
For Minh, this card is essentially a +3 during Mythos phase, or Unexpected Courage + card draw on her second action. For any user of Tooth of Eztli, this card basically ensures you pass any will or agility treacheries (and get the card draw), and otherwise functions as the seeker version of Quick Thinking - by which I mean rogues get ? plus an action, where seekers get ? plus a card.
It does seem that its best function is either going to be before your first action (during Mythos) or as your second action (for the card draw), although many with access to 0 seeker will find times for the third action use as well.
I see a lot of arguments against skill cards by comparing them to Unexpected Courage. I have never understood that, as there's no reason you can't have both.