They only need to fool laymen, and backdoored primes are an easy way to do so. The number of true cryptography experts beyond their walls is a dozen in the world at best. Case in point https://en.m.wikipedia.org/wiki/Daniel_J._Bernstein . And BTW he's been sued by the US government for ???. Thank God the EFF has decent funding.
This kind of logic is super common on HN threads and it's incoherent. If the expertise and capabilities of the NSA with respect to basic cryptographic mathematics is so unknowable that thousands of published academic cryptographers are wasting their time, then what makes you think a random amateur Math Overflow post has somehow stumbled on a deep secret of NSA RSA subterfuge?
For whatever it's worth to you, Dan Bernstein was not sued by the US Government. Dan Bernstein sued the US Government, over export restrictions on cryptography in the 1990s; his suit was mooted by the relaxation of those restrictions.
They’re the largest single employer of mathmaticians in the world.
At the same time, they negotiated DES's key length down. It was 64 bits originally, the NSA wanted only 48 bits, IBM and the NSA compromised on 56 bits.