Probably the proper translation out of geek-speak and into reality is that there is almost certainly no real structure that can be made purely out of Lego bricks that will cause the lower level to mechanically fail. (I'm hedging for safety. I really want to say there isn't one at all, but I've learned not to underestimate people's ingenuity. But let me point out by "real structure" I mean one that can be reasonably built in the real world, not, for example, a structure a mile high with millimeter tolerances made out of mass-manufactured plastic bricks.)

For another example, one could try to create an inverted pyramid on one brick to crush it, but it will topple long before it crushes the brick.

The structural strength under that circumstance (pure Lego, nothing else) is so enormously high, as determined by this experiment, that there's no reason to ever worry about this eventuality.

A counterexample is if you build a huge non-inverted pyramid and then put an extra brick in the middle on the bottom. It wouldn't balance but you could easily imagine putting many tons of weight on that single brick sticking out on the bottom like this, thus technically causing the lowest level to mechanically fail. This is pedantic, but I think you asked for it:)

Assuming the rest of the pyramid base doesn't end up flexing around that one brick (which would not be very tall) and distributing more of its weight on the ground...

Couldn't you use flying buttresses to stabilize the inverted pyramid without lifting weight off the bottom brick?

Well, sure. You can do all sorts of things. But you're still looking at stacking rather a lot of bricks on top of one brick.

I mean, were it just a matter of "a brick can support 100 meters of brick on top of it", I'd say, sure, obviously we can do that in real life. It'll be hard, but we can probably do it. But you have to put another ~1.5 orders of magnitude of pressure on... this is going to be "decidedly nontrivial", to borrow the mathematician's phrase. I'm not ready to say it's absolutely impossible, but it's in the "I'll believe it when I see it" class. That is a lot of bricks you are trying to stack on with no other failures getting in you way, and when you're dealing with that sort of accumulation of brick, micrometer variations you'd normally never even consider worrying about start stacking up....

You are correct, 3.5 Km is the maximum height only when building towers with constant horizontal cross section.

It's not even that, it's the maximum height for a tower of 2x2 bricks.

The guy who did the assessment said that he felt other shaped/sized bricks would be more or less able to deal with the pressure.

All on the BBC More or Less Podcast.

Yeah that had me slightly puzzled, you'd never attempt a tower with so few bricks as the stability would see it topple over quite quickly.

You are right but I'd prefer to have this answer as you can predict the maximum height of the tower that you designed using this. Also, a question that accounts for complex towers, would not be a question about legos much, I think.

The original Reddit question was simply "How many Legos, stacked one on top of the other, would it take to destroy the bottom brick?"

I would be interested to see how much stronger the 2x2 flat pieces would be.