The design flaw of the LDI seems to be how the LDI is linked to the same assets the pension funds need to sell off to meet collateral calls.
It creates a pretty death spiral where increasing gilt yield increase collateral demands. After a while the pension fund does not have enough eligible collateral (apparently long duration gilts are not eligible, which I find strange), so they need to sell gilts. This increases the gilt yield, which further increases the collateral needed for posting. Death spiral in full roll..
You could also say, if they didn't leverage the shit out of the LDI and kept more prudent levels, this would also not have happened. But like the article says, they probably did leverage the shit out of it, because they needed to free up a large portion of investments for higher yielding assets. The more allocated to other higher yielding assets, the more leverage in the LDI. Fascinating!