All characters are also the same size as CAPS so it feels like their websites are shouting at you.
I agree with that, but that is looks like that is the only way they can represent readable Kanji characters on computer screen. Making them smaller and lighter will make them indistinguishable.
On the other hand, this might have something to do with default japanese fonts we use, maybe there are better alternatives out there. Higher dpi fonts, perhaps?
"The problem that bothered them was this. Suppose the harried waiter cuts the pizza off-centre, but with all the edge-to-edge cuts crossing at a single point, and with the same angle between adjacent cuts. The off-centre cuts mean the slices will not all be the same size, so if two people take turns to take neighbouring slices, will they get equal shares by the time they have gone right round the pizza — and if not, who will get more?"
This is useful, of course, if you're familiar with the concept of "sharing" a pizza.
Numeric stability is probably not all that important when you're guessing.