What you're saying is mostly right, and in a practical sense is right, as well, but not as much from a technical sense. This is the specific block that is problematic.

Risc CPUs like the arm in the raspberry pi are really good at not doing anything, or doing a really small subset of things (it’s in the name!), but x86 is great at doing some stuff and being able to do a wide variety of stuff with its big instruction set. If you raise an eyebrow at my claim, consider that before gpus were the main way to do math in a data center it was x86. If the people who literally count every fraction of a watt of power consumption as billable time think it’s most efficient it probably is!

This is generally correct, per cycle. Overall, it really depends. The problem is, the x86 architecture does okay as long as it's kept busy and the work to be performed is predictable (for the purposes of look-ahead and parallelization). This is why it's great for those mathematical calculations you referred to, and why GPUs took over - they're massively better performers on tasks that can be parallelized such as math calculations and graphics rendering. Beyond that, the ARM use case has been tuned to low power environments, which means the computing does poorly in environments that need a lot of calculations because, in general, more computing requires more power (or the same power with more efficient hardware, and now we're talking about generational chip design differences). Now, couple that with the massive amount of money spent to make x86 what it is, and the relatively lower amounts that RISC and ARM received, and the gap gets wider.

Now, as I started with, even a basic x86 computer running at mostly idle is going to have pretty low power consumption, dollar-wise. Compare that to the power draw on a new router, or even a newer low-power mini PC, and your ROI is not going to indicate the need for that purchase if you have the hardware just sitting around idle. And it will still perform better than a raspberry pi configured to act as a router if your bandwidth is above about 250 mbps, if I remember correctly (and something like 120 mbps for the v4 and earlier generations).