I don't think so. The two posts I quoted talked about PC death being a reality without having to be likely, and about uncertainty, as sources of interest in a fight. Both these things can be achieved without resource consumption being a significant issue.response to pemerten:
"These posts give one illustration of how encounters can be balanced yet tactically meaningful within PC death being on the line to any significant extent: the abilities of the participants in a fight - both antagonists and protagonists - can be configured so that death is not a serious threat provided that the players play their PCs with mechanical and tactical cleverness."
But those examples were predicated on making the PCs use up their resources and how many resources get used in previous fights can throw off the balance of later fights.
I'm not sure how much 4e you've played. In my experience with it, it has a very high tolerance level for variations in resources relative to encounters: the players will adopt different tactics depending on how many dailies and action points they have left, and the encounter will therefore play out differently, but it's quite hard to "throw off the balance". The real action is in making decisions about how to deploy whatever resources the party has available, and this can be an interesting challenge even if the proper deployment of those resources is likely to guarantee victory. (And if the party is low on resources, the players will typically think harder about how to use what they've got - which increases the tension and the intensity, but needn't thereby throw of the balance.)
Another example comes from Rolemaster. In Rolemaster, melee combatants can get access to abilities called Adrenal Moves, which are a borderline between encounter and at will powers - when you roll to use an Adrenal Move, if successful you get a self-buff, if you fail a mild penalty. Succeed or fail, you can try again - but sustaining success faces an increasing difficulty, plus an increased penalty once you come out or fail. This mechanic generates an interesting tension in combat - "Should I use my Adrenal Move this round?" or "If I come out now I'll face a -40 penalty, but if I try and sustain I've only got a 50% chance of success and if I fail will face a -60 penalty - what should I do?"
This is not a mechanism that involves attrition at all, but it can make combat interesting without the stakes having to be so high that "the balance has been thrown off". It forces choices about how to act on a round-by-round basis, ensuring interest and tension. (It's also swingier than what would suit D&D, I think, but that's a general property of Rolemaster.)