I thought the reason was well known, and the article briefly touches it...

The liver's great ability to regenerate largely boils down to how homogenous and simple the liver actually is. It's structured more like a battery pack, where you have individual cells that are largely functionally identical to each other that perform the bulk of the work, and they happen to be connected together. If an individual cell fails, (for the most part) all you need to do is merely regrow a new one, and it's orientation matters little (relatively speaking as compared to other organs) so long as it's connected to the rest of the battery pack (organ).

Contrast that to something like a kidney, which has complex orientation that is formed via growth, and which has a high degree of different types of cells where replacing a part isn't as simple as merely regrowing the part which failed, but also about that growth happening in precisely the right location. So instead of it being like having to replace a failed cell in a battery pack, it's like replacing a wheel to a car. Attaching it anywhere (like the windshield for example) won't necessarily fix the issue, it needs to be connected to the axle...