I think you could do that, and the first time you did it might be kind of interesting (and it might work if deployed very occasionally too), but I think that if you kept trying to run the game that way, the way 5E suggests, the players would "get wise" to it and the game would become a lot more boring. Particularly because "getting wise" to attrition would mean players basically deciding, on a per-PC basis, to try and metagame so as to only burn two of HP/Stress/Armor before a Short Rest, and to burn Hope primarily in ways that supported regaining or not losing those things.
I think the idea of only burning two of HP/Stress/Armor works better in theory than in practice.
Sure, you could choose not to burn Armor when you get hit and take the damage to HP, but most PCs don’t have enough HP to make this a viable strategy. Likewise, burning Armor to save HP doesn’t work if you take any Major hits, which is possible even with weaker enemies.
Finally, PCs have very little control over not spending stress. Losing 1 stress is called out in the rulebook as a consequence of succeeding with Fear, and several enemies do Stress damage.
Also worth noting that the default encounter balance in DH is very different to D&D 5E. 5E does six encounters/day because the default "Normal" difficulty encounter is absolutely trivial (and Hard isn't Hard - unsure if 2024 has changed this), and only wears PCs down by inevitable damage/resource usage. The default DH encounter is more akin to a low-Deadly encounter in 5E terms, even if the DM isn't very aggressive with Fear usage (but equally doesn't just sit on 12 Fear).
A default « Standard » DH encounter may be low-deadly, but if you are running 6 encounters per day, I would expect that you would run a mix of Incidental, Minor and Standard encounters.
You have to burn more than 1-2 Fear per encounter because each Short Rest you gain 1d4 Fear, so you kind of need to sit at 8 Fear if the PCs are going to potentially rest, and given that 44% of non-Reaction rolls generate Fear, and encounters involve a lot of rolls, I think it'd be very hard to spend less than 3-4 Fear per encounter unless you were happy sitting on 12 Fear and wasting Fear (or you were starting out on like, 0-2 Fear - i.e. less than the normal 1 Fear per PC).
I suspect that in a six encounter day you would run a mix of Incidental, Minor and Standard Encounters.
Let’s say, 4 Minors and 2 Standards. You spend 1-3 on the Minors and 2-4 on the Standards (though to be fair, I agree with you that the estimates for these encounters in the book seem low). With those assumptions, at the end of the day, you spend 14.
On the other side of the ledger, you have no. of players + 3d4 + Fear generated by rolls. I think you could get less than 26 (14 + 12) with that calculation.