1.) Nvidia was getting densities of ~43.5M / mm² on 8nm compared with densities of ~119M / mm² on 5 nm, as you can see if you check various Ampere and Ada cards on TPU. So that is already almost 3X the density. And 3X may even be achievable considering logic scales better than cache and the newer Ada chips have a lot more cache.
2.) Even if all TSMC processes are too expensive, it doesn't rule out a newer Samsung process, such as their 5LPE node.
3.) Why did Nintendo decide not to build a smaller chip if their current one is wasting performance in handheld mode, and like you implied they only care about cost?
4.) Why is Nintendo apparently perfectly happy to design on a node that will likely be discontinued in a few years, forcing them to use a newer process anyway?
And regarding Ampere's performance, my point is that its real world performance is pretty close to GCN's, which was also considered to have "inflated" TF figures. So even a 2.4 TF Switch 2 should be enough to exceed the performance of the base PS4.