You can see from TSMC's own chip roadmap ... N4P (the advanced 5nm node) by TSMC's own labelling transitions to "middle-to-low end mobile" customers in 2024.
Take a wild guess which system is beginning manufacturing production and launching in 2024.
And TSMC knows all this stuff years in advance, Nintendo would have known this simply by talking to them years ago. As Apple leaves 5nm, a shit-ton of capacity for 5nm opens up. We can even see by 2026, the N3P (3nm) process will transition down to mid-to-low end range too (hello Switch 2 Lite).
Samsung may offer cheaper wafers, but the chip would be so massive on 8nm that you're not really saving any money. Even at $7k/wafer for Samsung vs $14k/wafer for TSMC, you have to understand the chips on the Samsung wafer are more than double the size (because it's 8nm) so per wafer you're getting like only 1/2 the amount of finished chips. A TSMC 4N wafer is going to be able to have double the amount of chips on a normal wafer because they're roughly half the size of the Samsung ones (again 8nm vs 4nm). And TSMC will have better yields on top of that.
Samsung is not charging less/wafer out of the goodness of their heart. They charge less because they know that on a node like 5nm you can get way more finished dies per wafer than you can on 8nm, they have no choice to charge less for 8nm.