"If everything has a backdoor, then why would NSA need to stockpile 0-day bugs? Why would they need such a big TAO division? If they had a backdoor they would just use that."

That argument is not true. Spy non-fiction taught me that intelligence services sort of rate their capabilities on what intel they can bring plus how secret they must remain. The idea being a capability might be so good and so hard to replace that you only use it on highest-risk cases that nothing else works on. Additionally, lower clearances will have greater number of infiltrators. They should see less than higher clearances to reduce damage of leaks. Further, I predicted that the tools themselves were developed in Special Access Programs (SAP's) that compartmentalized away from even TS clearances then selectively released to them. Sentry Eagle et al confirmed my prediction.

You can actually see the bullshitting in progress if you look at that. Each level of clearance is told something different with the lower levels often getting lied to with only highest getting the truth. In one case, it was implied they were attempting to use supercomputers against crypto then TS/SCI version said they got companies to backdoor it. Quite the difference. ;)

The GP post claims that every closed-source product is perpetually backdoored. If this were true, then there would be no way to detect backdoor access, and no way to deny it short of going 100% open source, which is simply not possible for large corporations.

What you describe is how intelligence services actually work to develop and protect real tools for access. What the GP claims is a fantasy in which such work is not necessary.

"The GP post claims that every closed-source product is perpetually backdoored. "

I agree that's a crap claim. Tried to provide alternative that showed situation is almost as bad as crap claims like that with 0-days. What overlap I did see was the emanation threat. That secrets leak out of any device and TEMPEST protection of them is illegal means that they are all backdoored for that in practice. Good news is it's a highly-specialist attack only a few countries know how to do that requires targeting and close proximity. Other good news is that smartcards and EM compatibility testing reinvented some defensive practices.