I agree on your last point, but I will say the P=NP feels like a particularly good candidate for being independent of ZFC, not only because it seems to be very

I agree on your last point, but I will say the P=NP feels like a particularly good candidate for being independent of ZFC, not only because it seems to be very difficult, but because it feels so adjacent to things like the halting problem and incompleteness theorems. :)