Regarding Simon and Speck: one simple answer is that the complicated attacks may exist and simple attacks certainly exist for smaller block and smaller key sizes.
However, it’s really not necessary to have a backdoor in ARX designs directly when they’re using key sizes such as 64, 72, 96, 128, 144, 192 or 256 bits with block sizes of 32, 48, 64, 96 or 128 bits. Especially so if quantum computers arrive while these ciphers are still deployed. Their largest block sizes are the smallest available for other block ciphers. The three smallest block sizes listed are laughable.
They have larger key sizes specified on the upper end. Consider that if the smaller keys are “good enough for NSA” - it will be used and exploited in practice. Not all bits are equal either. Simon’s or Spec’s 128 bits are doubtfully as strong as AES’s 128 bits, certainly with half the bits for the block size. It also doesn’t inspire confidence that AES had rounds removed and that the AES 256 block size is… 128 bits. Suite A cryptography probably doesn’t include a lot of 32 bit block sizes. Indeed BATON supposedly bottoms out at 96 bits. One block size for me, another for thee?
In a conversation with an author of Speck at FSE 2015, he stated that for some systems only a few minutes of confidentiality was really required. This was said openly!
This is consistent in my view with NSA again intentionally pushing crypto that can be broken in certain conditions to their benefit. This can probably be practically exploited though brute force with their computational resources.
Many symmetric cryptographers literally laugh at the NSA designs and at their attempts at papers justifying their designs.
Regarding NIST curves, the safe curves project shows that implementing them safely is difficult. That doesn’t seem like an accident to me, but perhaps I am too cynical? Side channels are probably enough for targeted breaks. NIST standardization of ECC designs don’t need to be exploited in ways that cryptographers respect - it just needs to work for NSA’s needs.