You don't need a gap to be created. That is where your thinking goes wrong. The upper and lower knees of the buckled columns will collide.
That is exactly where your "reasoning" falls off the rails Tony.
I cannot help you if you refuse to think BUT....
..I'm stubborn and I am right on the key issues of explanation.
You scenario of "knees" which "collide" continues to presume that one knee is above the other - coming down onto it - there again you create your phantom gap. The central error you continue to make. In reality there was no gap. Let's look at what really happens.
In forming the "knees"
* the process of forming knees actually moves the two "ends" past each other. They are already bypassing as part of the process of forming the "knees". By the time the knees have formed they are already past each other.
PLEASE do yourself a favour. Sit down and quietly think through what happens for any
one column. Use a stick of plasticine OR Draw it on paper and - as the top load pushes the top end of column down go step by small step through the sequence. How do the bits of the column reshape and realign as the buckling progresses to form "knees"?
Remember that the top and bottom of the column are getting closer together. Overall the column is getting shorter as the top structure load pushes it down to fail in axial overload. Resist the temptation to only consider one factor at a time. So where do the two parts of buckling column go as they bend into "knees"? There is no gap.
And do it for ONE column at a time.
Given the number of years you have harboured your false understanding it will be a big step BUT if you can make that large leap in conceptual understanding for one column it will be a lot easier to build up to more columns.
There will be another step increase in understanding needed at the stage where you start to quantify the engineering from collapse of a single column to incorporate several adjacent columns in a load redistribution setting. The thinking effort becomes easier after that second stage.
BUT stay with the one column first stage of thinking until you get that right - without the need to continue inserting phantom gaps.
The column folds through getting shorter as the load presses down. There is never a gap.
AND: * There may have been other mechanisms BUT they do not change the overall logic. Lets stay with the most obvious one first