I've seen a few posts implying that Ampere is too expensive or too new for a Switch successor. Ampere is not state of the art. It is two architectures old as of the launch of the RTX 4090. Hopper (Datacenter) and now Lovelace (Gaming) has launched after it. Depending on when the next Switch launches, it could be three architectures old.

I think the calculation for the System on a chip is a very different one than for a High-End-GPU. The process node for Orin (8nm Samsung, what Nvidia used with the Ampere RTX 3000 series) is now an older node and Samsung struggles to keep their customers, with the RTX 4000 Nvidia switched back to a custom TSMC process node called 4N, which is an optimized version of their 5nm-process. Mobile Chips (outside of big Notebooks) are way smaller than a dedicated GPU, which reduces the rate of defect chips and makes them cheaper. Another aspect of the SoC-cost is the license-fee for the ARM-CPU-Cores. All in all Nintendo wants to break-even in the beginning and make a small profit, but they will make their money back in the following years in the same way they did with the current Switch by growing their margin and releasing revisions which reduce cost.

I had a look at the wikipedia-page for Nvidia Orin and found a rather interesting entry in the specification-chart:

The big chips in the Orin-Family are using way too much power, 15-60 watts(AGX Orin 64GB) or 15-40 watts(AGX Orin 32GB) would melt the current Switch. Even 10-25 watts (Orin NX 16GB, 1024 Cuda Cores like the rumored T239) would be too much if they don't want a bulky handheld like the Steam Deck. Orin NX 8GB could be the base for the custom chip Nintendo wants, 10-20 watts under full load, but we know Nintendo likes to run the chip a bit slower to save power. Give it a bit more ram, maybe some additional tensor-cores for increased DLSS and run the CPU-Cores on 1 GHZ like the current Switch. Use the tensors to decompress data in loading screens and save energy by not increasing the CPU-clockspeed (current Switch does this in some games to shorten loading times). Memory bandwidth, which was a real bottleneck in the current Switch, could be up to 102.4GB/s, combined with advancements in texture/data compression this should be enough for going beyond 1080p.

If they don't bodge on the memory this could be a really good generational jump. Even at same clockspeeds you would have two times the CPU-Cores and four times the GPU-Cores, which both are much more capable in a 1:1-comparison. Additional Tensor- and Raytracing-Cores.  Two to four times of RAM-Capacity with up to four times of memory-bandwidth.

I would buy that Next-Gen-Switch on day one to play Zelda on it.

Seems a reasonable expectation, but the jump do seem smaller than common between gens even more for the long period between systems.