Board costs are more or less fixed. The chip is on a new node right now so it's expensive but it'll go down. The talk about new node wafer being $15,000 might be true in the beginning but after some time it won't be that much more expensive compared to older nodes. There might be a point where the upfront cost is high even for Nvidia but that's not how it is currently.
Cost isn't just about components either. As time passes the engineers will find a better way to do things and lower cost. Volume leaders like TSMC really benefit from this.
Optimization such as for memory bandwidth(among other things) also benefit the lower end more. Otherwise they'd have a high fixed(board cost). In the mobile space, it'll result in less power needed to transfer per bit. Caches for example are very power efficient.
That's not how it works. Costs can go down if the issue is low yields, but the reason for the cost increases is that these smaller nodes need more manufacturing steps that probably can't be reduced.
Yeah, unfortunately the last two nodes have seen cost increases for the the wafers. In the past the wafers would essentially cost close to the same as they did on the last node, and with the manufacturing node allowing more transistors per square inch on the wafer, it would cost less to create the same chip/circuit on the new node since it would take up less wafer space (and thus more chips could be printed on the same sized wafer increasing yields over the cost of the materials). That hasn't happened the last two times, with the costs of the new wafers and the manufacturing costs being higher much higher than the older nodes. We have been lucking out in that the performance increases are still higher than the price increases, but things are getting tighter.
This is one of the reasons I think AMD with their chiplet design is going to really start to take advantage of the current situation. By using the latest manufacturing node for parts of the chip that can benefit from the new processes, while using older nodes that are cheaper for pieces that do not benefit from the smaller node (such as cache memory and I/O interfaces), AMD can take advantage by not needing as large of a chip to be error free on the new manufacturing node, as they are using one or more tiny chiplets instead of a 2-4x the size larger monolithic die. This means less wasted chips per wafer, increasing their yield rate over their competitors (Nvidia and Intel), which in turn means a less costly GPU (or higher profit margin). As long as AMD decides to build a top of the line GPU off their chiplets, I think they have a real chance this generation to start outperforming Nvidia.
Nvidia is also paying a premium to get back as a customer for TSMC this time around after dropping them for Samsung for the last consumer generation, and probably learning their lesson that the grass is not always greener with the manufacturing difficulties that Samsung had for producing the chips in volume. Where-as AMD is simply continuing its already existing business relationship with TSMC and probably has a much better deal for remaining a loyal customer (especially since they make no only the GPUs but AMD's CPUs as well).