In the past decade, I can think of 2 sort of new general cryptanalytic attacks: invariant subspace attacks, and the division property. The division property didn't really break anything; it claimed a full break of MYSTY1 with complexity 2^70, in case you happen to have the entire codebook already. It doesn't work well mostly for the same reason cube attacks haven't: most cipher designers know how dangerous a low algebraic degree can be.
The invariant subspace attack has been more successful, mainly in the lightweight space, mostly because it exploits the symmetries that tend to make a design smaller and elegant. But once again, against vetted ciphers it has not done so well.
So let's posit the NSA does have another couple of attacks in hand we don't know about. Chances are they're not going to be very useful. Do they specifically affect SIMON and/or SPECK? It would require an intersection of conditions that seems very implausible, and it seems tricky to have it affect both designs at the same time without being noticeable. But I guess we'll know in 2027.
In another note, if I was going to make a cipher with a hidden weakness to dupe the world into using, I probably wouldn't go with a block cipher---literally the most heavily analyzed kind of primitive in the public sphere. I would probably go with a stream cipher, or a stream-like dedicated authenticated cipher, whose security is much less studied than block ciphers, and can still be used in most places a block cipher would be.