In the Fallout lists for Dogs in the Vineyard, a lot of the options revolve around losing things: dice from Stats, belongings, relationship dice, etc. However, some of the options are something like "take a new trait at 1d4."
Given that traits give you dice to be rolled in a conflict, why is this a negative consequence, such that you'd want to avoid taking Fallout?
This is predicated on the idea that DitV isn't a mechanical game, it's a psychological one.
Yes, you get more dice for failing. Fallout can be made part of the advancement process. There are a lot of ways to game the system, and it doesn't care. DitV has no interest in mechanical balance or sense. Instead, DitV is balanced around being interesting (in the creator's sense of the word) and its mechanics are all molded to that whim.
Your d4 from Fallout is probably going to be attached to something… unfortunate. So in order to use it, you'll have to force your Dog to keep poking that old wound, whether physical, social, or emotional. Remember:
When you take a Relationship with a person, you’re saying that you want to be in conflict with him or her. (DitV 98)
Now your d4 is sitting there saying "To use me, you'll have to embroil yourself in that conflict again!"
Stockpiling d4s is negative because sitting at the table with a bunch of d4s is going to tempt you to stay in when all you're going to be able to do with them is take more blows.
In that way, it's almost like a pre-compel in Fate: I'll give you this Fate point now if you promise to do something stupid later.
Remember: interesting, emotionally wrenching, philosophically challenging stories are the real goal of the game, and it does this not through mechanics that force you into such situations, but through mechanics which manipulate you into them. In that context, d4 Fallout makes perfect sense.
The game wants you to take the blow. If it punished you for taking the blow, you wouldn't do it, and the game wouldn't get what it wants!
Don't treat the various options on the fallout tables as balanced or equivalent. The option to lose a die from a stat, for instance, is obviously way worse than the option to add a new d4 trait. Taking a new d4 trait is a mechanical improvement, as you point out. This may mean that when you take fallout, you always ignore the other options and always only take new traits. This is fine, it won't do the game any harm for you to do this.
Fallout is the consequence of conflict, not necessarily a stick to drive the players. (That's the role of stakes--make them fear losing, to the point that they're willing to take fallout to prevent it from happening.)
As a Dogs GM, fallout should be appropriate to the circumstances--be sure that you lead with the story, then work out trait damage, or whatever else results. (I know that I often fell short at this as a GM; too many habits had me keeping characters sacrosanct in their players' hands instead of actively challenging and encouraging hard choices in fallout. It's even better if all of the players actively treasure verisimilitude and chide their fellow player about taking a cheesy d4 trait after getting a shotgun blast to the gut.)
The book has an excellent example of an appropriate d4 fallout trait--when you finish confronting your brother, humiliate him, and send him home without his gun. That relationship is established solidly as part of the fiction--he's not happy--so a d4 makes total sense, even though it's lower than the typical d6 for blood.
D4 fallout is also great for traits reflecting temptation, "The bottle soothes my righteous rage d4", or showing how your character is changed by your experiences, "Only a shallow reader of the Book of Life, d4" or "Twitchy about canyons, d4". They're also great where fallout comes from losing an argument. Maybe their argument has changed you... which is scary when a sorcerer persuades you!
