I agree with some of your points, with the exception of actual stock levels.
I have seen wild assertions of single digit allocation for a large country/consumer base which is patently false.
Also, worth mentioning, OEM always get first dibs on parts, not just GPU, but chipsets and CPUS as well.
It is easier and far more profitable for AMD/Nvidia/Intel to sell bulk pack/Tray/etc products to an OEM like HP/Dell/etc than to DIY users, this is purely due to scale and lack of end user support.
Thats the same way you see that even when consumer CPUs can be on shortage, there is rarely a shortage for enterprise... This is because there is a tiering system in regards to allocation, and all companies involved know what their bread and butter is.
This is not just electronics either, for example, I spent a decent stint of my career working in automotive which I guess would explain why I tend to lean into parallels with that industry.
But, we have all seen "fleet vehicles" and just so you know, i have seen when parts such as transmissions or engines were on shortage at GM, and they opted to equip base model stripped down fleet vehicles versus building consumer cars where they make more profit. The reason is, they know who pays the bills at the end of the day and less hassle to deal with as well.