Via what mechanism is such load-sharing supposed to take place? A typical building may be roughly modeled as a cubic lattice with some added diagonal struts (let's assume the primary struts run n/s, e/w, and u/d). The floor construction is highly resistant to tension and compression in the ne-sw and nw-se directions, since people generally don't mind floors that are solid. The number of struts or equivalent running in vertical-diagonal directions, however, is much smaller. While it would probably be possible to construct a building where the space of every tenth "floor" was largely obstructed by diagonal supports, and such a building would be capable of withstanding considerable structural damage without collapse, I'm unaware of such construction being anything even remotely resembling common practice.
“Via what mechanism is such load-sharing supposed to take place?”
It not only is “supposed to take place”, it does take place (in most high-rise buildings), because the horizontal-beam components, upon which the weight of the floor rests, are not just tied to each other and to the columns on the perimeter-external wall, and the core, they are, at various points in their horizontal structure, tied to the many intervening vertical columns between the vertical columns on the perimeter-external wall and the core.
The weight-load of the floor is thus spread/carried, collectively by all the vertical columns. Because there are multiple such vertical columns, between the perimeter-external wall and the core, there could be a small number of failures at a number of individual vertical columns, at the perimeter-external wall, or in-between the external-wall and the core, and the weight-load of the floor would still be supportable, with all the intervening and surrounding vertical columns carrying the additional weight of the floor that is no longer supported by the few damaged vertical columns (or damaged connection of the horizontal-beams to the vertical columns) under that particular floor.
The WTC towers had no such intervening columns between the perimeter-external wall and the core. The horizontal-matrix under the floor is capable of remaining rigid, across the totality of the floor, if it is not itself damaged. But, it is not capable of remaining at the same position, vertically, across it’s entire expanse, if too much of it’s weight no longer has connection to too much of the vertical supports.
The more the number of such vertical support points there are in the structure, the less weight needed to be “carried” independently by any one vertical column. This same principal can apply along any horizontal axis of the floor. But, in the case of the WTC, there was nothing that supplied primary vertical support between the perimeter-external wall and the core - nothing that would help, temporarily, carry the weight-load of the floor if vertical support failure occurred at the external wall and the core.
In a conventional building the loss of too much of that vertical support - to a floor at the position it is at, vertically - by which a floor would “drop”, requires damage to connections to many vertical columns between the external wall and the core, because there are many vertical columns that can temporarily carry the load displaced to them from a few that are damaged.
The WTC had primary vertical support for the floor-sub-structure at only two general areas - the vertical columns at the perimeter-external wall and the core. The attack damage and the fire damage, together created breaks, heat-stress and disconnections to some of both areas (the subfloor’s connections to vertical support) for the floors that received the direct hit.
Without any intervening vertical columns - between the core and the external wall, the weight-load for the sub-floor areas with there direct connections to vertical support dam aged meant that their weight-load was transferred along both horizontal axis to where-ever remaining vertical support still held - which, again, at the WTC could only be at the perimeter-external wall and the core (nothing was in-between).
You can see this load-shift/transfer to the vertical supports at the perimeter-external wall, in the last few seconds just before the collapse begins, in the form of wave-motion beginning just at and under the most-damaged floor and spreading upward.
The undamaged vertical columns at that point are trying to respond to the weight-load being transferred to them from the horizontal sub-floor structure. It must be transferred to them because where that structure no-longer has vertical support, it must either fall, or achieve its present position, by transferring the load horizontally to other perimeter-external columns or the core. But, at that point heat-stress had also begun to damage some connections of the horizontal-sub-floor structure at their points of connection to the core. At that point, you then had some (apparently too much) weight of a damaged floor no longer tied to vertical support at the only two vertical support areas - the perimeter external wall and the core.
That’s when the “pancake” affect began, with each floor that “dropped” adding its weight to the total weight load needing vertical support under it and ripping at the core as it “fell” - in other words, the weight load requirement became 2x, 3x, 4x, etc, as one, two, three floors , etc dropped onto the “next” floor.
Personal experience of a friend of mine witnessed the logarithmic scale of the increasing weight-load of the “pancake” - as he described the sound as similar to a monstrous freight-train careening off of its tracks at a constantly increasing rate of speed - he could hear the rate of the fall increase as it proceeded (he was there, escaping to a distance of a couple blocks from the building before the fall).