I see the discussion leaping between two neighboring but separate facets of Consequences. Someone makes a good point about one facet, then someone brings up the other facet as counterargument, and they aren't really the same.
Consequences serve two distinct purposes:
1) Fate Point Generator: this is *good* - it can sting taking that first free tag on a Broken Leg, or Town Pariah, or Crippling Self-Doubt, but after that, the GM has plot hooks, and the player gets Fate Points. All those complications from having a Consequence which lasts for awhile ultimately contribute to drama, narrative, etc. And if the player can throw a few Fate Points at one of his own Consequences? Brilliant! Strength through adversity. Some people planning to Concede a conflict may even opt to take a few Consequences just to build up some Fate Points (you get one for every Consequence you take in a conflict for which you Conceded).
2) Ablative Narrative Armor: this is the part that really chafes - the fact that a Consequence taking up a slot in your Consequence track may mean your character will be more liable to fail in a later conflict, one which may be unlike or even completely unrelated to the precipitating conflict. But that is what Stress in DFRPG ultimately measures: a character's narrative agency. It might seem like armor and hit points, but it isn't. It is your treasury of plot impact, and it can be squandered or gambled just like any resource, and yes, it may sting later. But there is a mechanism to mitigate that sting: Concession.