Did you watch the gif play?

Did you see how the structures on the roof collapsed first straight into the building?

Because if you miss that you're going to be off on this

as to hide the simplicity of the conservation of energy argument

Because. A. You won't see the full collapse process And thus B. The timing will be completely off

C. Free fall does not describe the full collapse sequence. It describes a portion of the end of the collapse sequence for about 2 and 1/2 seconds

The left side of the roof seems to collapse about 4 seconds before the rest of the building itself collapses.

To simplify this if you have a 50-story building. And the support structure is on floors 5 through 10 are completely destroyed. Floors 30 to 50 are just simply going straight down. As you noted, potential energy becoming kinetic energy at that point.

Here's how an engineer described what I'm trying to say about the roof. https://www.canadianconsultingengineer.com/features/the-collapse-of-wt-7/

At about 5:20 p.m., the collapse sequence began. First, the east and west penthouses disappeared from view, followed by progressive collapse, apparently on a lower floor. Videotapes show the upper 30 to 35 stories appearing to descend intact, indicating the collapse was initiated on a lower floor. Just before the collapse, a crack or “kink” or fault line developed along the north wall in the vicinity of the east penthouse located over transfer trusses 1 and 2 on the east side.

And kudos to making a scientific argument on this topic. It's refreshing.