Why is the situation where an whole atom doesn't obey the Pauli exclusion principle much more exotic and unusual?
I mean, take a look at the wikipedia pages https://en.wikipedia.org/wiki/Composite_boson and https://en.wikipedia.org/wiki/Composite_fermion - when one talks about composite bosons, it's exotic materials like superfluid helium, bose-einstein condensates, cooper pairs.
Since it's only a even/odd difference, I would expect that roughly half materials form composite bosons, and the other half form composite fermions, but this doesn't seem to be the case.