I was under the impression that it used a particular type of USB-C cable, but maybe I am wrong. AFAIK the reason the microcontrollers are expensive is because it is an Intel/Apple proprietary standard, which could be changed. Dunno about RF, I would have thought a USB cable would have been more shielded than a PCIe riser or a SATA cable.
Yes, a particular kind with bespoke chips in each connector and very high requirements for shielding and signal integrity, as well as quite short maximum lengths.
As for the controller, TB3 is integrated into USB4, so that could theoretically be used, but you're still adding a relatively expensive high speed I/O controller just to transfer an already existing PCIe signal which could be transferred natively with a riser or u.2 cable. Why overcomplicate things by adding unnecessary hardware?
Distance. Thunderbolt can be run further distances than PCIe alone by itself.
To a degree - PCIe 3.0 can be run impressive distances with just passive risers. 4.0 needs tons of shielding and very high quality cabling though. TB3 tops out at, what, 3m, though in real life more like 2m due to there being no available cables? Active/optical overcomes that, but then you're looking at cables costing several hundred dollars, which kind of defeats the purpose.
Is there noticable RF inside a computer case?
Tons. The main reason PC cases are metal is to contain the RF noise they emit to avoid it interfering with other devices. High frequency signaling through board traces or wiring gives off noise; coils and power conversion gives off noise, your CPU and GPU operating at several GHz will give off noise, etc.