From what I understood
Hot temperatures --> ... --> Columns sag --> ... --> Local stress exceeds local strength at exterior column/floor column connection/s --> ... --> The first floor collapses --> ...
Are you telling me this is wrong?
Yup. By the scenario that you've posted (just fires), the towers would, to a very high probability, both still be standing.
I know that you know there was more than just fires, but this is EXACTLY the perennial mistake that truthers make: picking out only one of the significant factors. Such as "fire never caused a steel framed building to collapse." (Both over simplified and wrong.) Or "the buildings were designed to withstand an impact from a jet." (Both over simplified & wrong.)
Here is one very important consideration that you've left out. Read it carefully & try to understand what it is saying.
Bazant
The effect of stress level on creep.
Journal of Engineering Mechanics ASCE , Vol. 134 (2008)
What Did and Did not Cause Collapse of WTC Twin Towers in New York
Zdenek P. Bazant, Jia-Liang Le, Frank R. Greening and David B. Benson
Page 2:
Bazant said:
"But are high steel temperatures really necessary to explain collapse?
Not really.
... The tests by NIST (2005, part NCSTAR 1-3D, p. 135, Fig. 6-6) showed that, at temperatures 150° C, 250° C and 350° C, the yield strength of the steel used in the fire stories decreased by 12%, 19% and 25%, respectively. ... These effects of heating are further documented by the recent fire tests of Zeng et al.(2003), which showed that structural steel columns under a sustained load of 50% to 70% of their cold strength collapse when heated to 250° C.
... Nevertheless, it can easily be explained that the stress in some surviving columns most likely exceeded 88% of their cold strength S0 . In that case, any steel temperature ≥150° C sufficed to trigger the viscoplastic buckling of columns (Bazant and Le 2008). This conclusion is further supported by simple calculations showing that if, for instance, the column load is raised at temperature 250° C from 0.3Pt to 0.9Pt (where Pt = failure load = tangent modulus load), the critical time of creep buckling ... gets shortened from 2400 hours to 1 hour ...
Therefore, to decide whether the gravity-driven progressive collapse is the correct explanation, the temperature level alone is irrelevant (Bazant and Le 2008). It is meaningless and a waste of time to argue about it without calculating the stresses in columns. For low stress, high temperature is necessary to cause collapse, but for high enough stress, even a modestly elevated temperature will cause it."
You've left out some fundamental things that would have completely changed the outcome.
loss of insulation
physical damage from plane impact
greatly increased stresses as a result of damage
the enormously increased rate of creep because of the high stress levels
What this means:
To a very high probability (not a certainty, there is disagreement on this)...
Just the fire, no physical damage => no collapse. (IMO. Dr. Quintiere disagrees. He's an expert. You'd do well to listen to him. But I still think I'm right.)
No physical damage from the plane crash means that the insulation would have been intact & the stress levels would have remained their low, "as designed" values.
The columns would not have gotten as hot before the fires burned out. At the "as built" stress levels (1/2 to 1/3rd of strength values), you would not have had as much or as rapid creep. Or as much load shifting between core & perimeter columns.
Just the physical damage, no fire => no collapse. (IMO, highly probable from the fact that the towers restabilized themselves after the initial impact.)
You said: "Parts (including floors) don't fail because of "sag""
But isn't "sag" an important step in the cause of collapse?
I mean exactly what I said. Parts do not fail because of "sag". They fail because of stress levels exceeding strength levels.
What determines stress levels: Amount of load, direction of load, cross sectional area, stress concentrations (like discontinuities, sharp corners, features like holes machined into parts, etc).
And, in a lattice structure like the towers in which lots of elements simultaneously carry a load, if some parts shed their load, then it has to be borne by the other elements. In this way, increased temperature can both increase or decrease load (& stress in a member). Higher temps can increase stress by lengthening the columns (thermal expansion), thereby causing the longer ones to take up more of the load. Increasing temperature some more can cause the column to creep (i.e., essentially shorten), thereby decreasing the stress.
What determines strength? The type of load (columns are very strong in pure compression, very weak if loaded in bending), material & (especially) temperature.
And, as Bazant's research above shows, (progressive, sometimes runaway) creep is a function of both temperature & stress levels. Creep changes the geometry of the building. (Sag is a form of creep.)
Changing the geometry of the building dramatically changes the loading conditions. If you lose the balanced geometry & the balanced loads & the balanced stresses that result, then you'll lose the building.
How then is my original question meaningless, as you like to put it?
See bold part of Bazant's statement, above.