I cannot see the reason, and it seems to develop pulley way faster than if the underside of the key is flat.

I agree that the key have not a precise fulcrum point, it moves on the balance punching, but that conical hole is just adding wear in my opinion.

The German model is adjusted precisely and does not take so much play (pulley) with time.

Some result with the moistening of the wood in the hole with 70% isopropyl (30% water). Not perfect, but a real amelioration (did 3 times on some keys) . the trick is very efficient on Japanese keyboards.

Is it related to the rounded balance rail used only on the US accelerated actions? Perhaps this is why you don't see it on the Hamburg pianos.

Thank you Grotriman, the instrument is before 1890 and the keyboard does not have the round parts I have seen on the accelerated action.

Even then I don't figure how putting the contact point of the balance pin a few mm above the bottom of the key can help ? The balance makes an oblong path in the hole, due to the conical shape inside of the key I understand the contact can be kept, but why raising the bottom of the hole, I cannot figure.

the hole may be oval then. I want to understand that because if I ream that kind of hole I have to understand what is the effect of the reaming.

On German Steinways (new/recent) I use a modified rat file and work only a small part of the hole, just where the pressure is, not enlarging the other side, That is how the key can stay tight during the stroke.