First thing I want to look at, how good is the card without the attack bit? Terminal nothing now, Hunting Grounds next turn. Or, I think a useful thing for duration cards, playing one every turn is like playing.... a smithy every turn. But you need to get two. And this misses the shuffle more than smithy. And it costs 5. In return, you can maybe set up something where you're getting some monstrously good hands and some very mediocre ones - but I find that, at least with most of the other duration cards, I much prefer having them split than gobbed up together. (Tactician is the obvious exception)
I've been thinking about this. Let's call "Woods" the non-attack part of this card.
First thing, how many Durations miss a reshuffle due to their Durationiness? On average, exactly as many as the average number you play each turn*. So, if you play a Woods every turn, you will need to buy one more than if it didn't stay on play until your next turn.
*The well-known corollary to this is that, in a draw-your-deck engine, you need twice as many Durations as you intend to play every turn.
But!
To play a smithy every turn, you need to have smithy in your starting 5 card hand. While to play a Woods every turn, you need to have one in your starting 8 card hand. If we use the naïve approximation of buying 1 smithy per 5 cards in your deck and one Woods per 8 cards in your deck to allow playing one per turn, that means that for a 15-16 card deck you need just as many for both, and for a 24-25 card deck, you need one less Woods than smithies.
Buying less Woodses than smithies for larger decks is a double advantage: you can spend those buys and coins on other useful cards, and you will have less dead actions limiting your buying power (those dead smithies in your hand could have been a silver, etc.).
All this (and the possibility of using it as a pseudo-tactician) is likely not enough for Woods to jump from $4 to $5. But it's definitely not worse than smithy when playing one per turn.