I've been meaning to write some general musing on the Duration Type all week, and I'm just now finding the block of time to do it.
I'm going to simplify the Duration type a little, and say that a Duration card has three effects: "on-play", "while in play", "next turn". Outpost is a bit of an outlier here, so I won't worry about it. In particular, I'm not going to address cards which hypothetically stay out for three or more turns. I'm sure a few of these will be submitted, and I hope they are being designed for a reason and not just for the hell of it.
Of these three effects, only Lighthouse does the "while in play" effect. This is really an interesting area to explore for card designs in my opinion, although I did not submit such a card. Effectively, Lighthouse uses the Duration type to get a "between turns" effect, which is pretty cool.
Now, aside from enabling the "between turns" effect of Lighthouse, and I suppose the "triggers at the end of this turn" effect of Outpost, what new design space is really opened by Durations? (It is really borderline whether Outpost needs to be a Duration card. Effectively it is left out to remind you, immediately upon finishing your turn, that you should take a new turn. But come on, no one is about to forget already, and there would be no confusion about how Outpost is intended to function.)
What I stated earlier in the week is that Durations mostly allowed the printing of a bunch of vanilla cards. Well, after thinking this week, I've noticed that there is something more. Firstly, I want to propose that the Duration Type is, generally speaking, a nerf. A penalty.
The most often discussed penalty is that they miss the reshuffle more often. This is overblown in most decks, but as you get closer to drawing your whole deck, it becomes more severe. In most decks, Lighthouse is effectively as much economy as Silver due to the "overlap effect". If you play one Lighthouse per turn, then the overlap of their coins produces $2, so it is like playing a Silver each turn but also protects against attacks. But if you draw your whole deck, then it is taking two cards in your deck to provide the economic output of just one Silver. That is, if you'd bought two Silvers rather than two Lighthouses, then once your begin drawing your deck you'd have $4 per turn rather than $2. Similarly where having purchased 6 Wharves only allows you to play 3 Wharves per turn on average. This is a nerf relative to Wharves which don't have to stay out, yet still give the next turn effect.
But another nerf is the delayed bonus. But is this really a penalty? I want to argue that this is a big part of why all current Duration cards have a weak effect now and a strong effect later. Consider Wharf. The "this turn" effect is +2 Cards, +1 Buy. That would be a $2 card, maybe $3? At $3, you'd probably buy it often enough to put into an engine for the +buy. But there is no way it is a $5. But what about the "next turn" effect? It is essentially equivalent to playing "+1 Action, +3 Cards, +1 Buy". That is nuts! How much would a card like that cost? Absolutely more than $5. Probably more than $6. It is starting to get to the price range of Province, which begins causing issues of its own. And it just isn't exciting enough to exist at $7 or $8 or whatever price it would need. The Duration Type is a penalty which allows otherwise too powerful effects to be published. But the real beauty is that it doesn't feel like a penalty. Since the payload comes later, it feels like you're getting an awesome bonus.
You buy the Duration cards for their later effect, which in every case is considerably stronger than their immediate effect. If this lopsidedness were reversed -- if the effect now were better than the effect later -- then it would wouldn't work out as nicely. If Wharf were $8 card good now, and $2 card good later, well I'd argue that the cost of Wharf would have to be closer to $8 than it is now. Sure, it will miss the reshuffle more often, but it doesn't have that delayed gratification nerf. In fact, reshuffles aside, the Duration Type is something of a bonus on this bizzarro Wharf; it would probably have to cost more than $8 rather than $8. So a "strong now, weak later" Duration card would cost more than the strong effect, rather than less, which does not help to expand the design space. You'd be better off just printing the strong effect without the tiny later bonus.
Of course, with the Wharf example, the strong effect leads to drawing your deck, so the reshuffle issue is more acute. Imagine instead a Duration card which is "Pearl Diver now, Familiar later". That card would be worth less than Familiar. On the other hand, "Familiar now, Pearl Diver later" would tend to be worth more than Familiar. Yet despite being the stronger of the two cards, I think the latter feels less fun. Man, I already got the payload out of the card. I'm not that motivated or excited about it staying out an extra turn. In the former card, I am excited about the card staying out so that you'll get a fist full of Curse in your face next turn!
Now, you could try going a bit further. Not just "strong now, weak later" but rather "strong now, penalty later". Now we are weakening the card some. "Familiar now, I discard down to 3 next turn" is worse than Familiar. You could try doing something like a front loaded Wharf by saying "+1 Action, +3 Cards, +1 Buy now, I gain a Curse next turn". But man, why? The published Wharf feels so much more fun to play! It's feels like I'm getting a bonus, rather than a penalty. Now, some of the published Durations are essentially "penalty now, strong later". Specifically Haven, Outpost, and Tactician. But even with Tactician's super harsh "discard your hand" penalty, the reward you get later on is so attractive that you hardly mind. A roughly reversed Tactician, "+2 Actions, +6 Cards, +1 buy now, discard your hand at the start of your next turn" would be much less fun (add in something to prevent playing multiple Tacticians in one turn).
So in summary, the Duration Type allows you print very powerful effects at reasonable costs by causing the effects to be delayed and blind. This, in my opinion, is one of the key reasons that the published Duration follow the structure of "weak now, strong later".