I am mystified of your column/column connections and tray/column connections - if they can resist the transverse test, and if the structure will stand by itself with your heavy, solid trays, &c.
No great mystery. The columns only span one floor. Each tray has two sets of columns attached to it, one set extending downward to the tray below and one set extending upward to the tray above. Those columns do not meet end to end.
This is not so unusual. A lot of things (including most frame built houses) are built with vertical members that are only the height of one floor, and where each floor supports the columns for the next floor up instead of column ends bearing directly on lower columns.
That means that if the floors collapse the columns collapse with them. There are no long continuous columns to remain standing.
As I said, that is different from the WTC towers, which did have long continuous columns. But the columns in the WTC towers couldn't remain standing once the floors collapsed either. There's a different reason for that in the towers, but the result is the same; the columns cannot stand if the floors fall.
Respectfully,
Myriad