AT&T and Verizon don't have 'plant' employees. Much simpler - and legally, safer - to just give the bag of money straight to the corporation.
Risk of refusal. Risk of intentional or unintentional leaks.
As for other friendly and less-friendly nations, I'd be very surprised to learn that there weren't any other nations represented in the ranks of Intel engineers.
E: ah, TIL. https://en.m.wikipedia.org/wiki/Rubber-hose_cryptanalysis
That said, the main hurdles seem to be managing people and funds, which government agencies seem pretty good at figuring out. So maybe not all that easy, but maybe not particularly hard either. The biggest problem might be keeping it secret, given the number of people that might need to be involved that are clandestinely working for a TLA but not as their main job and not steeped in the culture of secrecy.
Yes, very unlikely. Something like the Intel Management Engine would be a much easier target.