Since armadillos in the U.S. can carry leprosy, I think I would have to be really hungry to eat them. Yes, I know it's only 2-5%; yes, I know it usually takes repeated contact, but.....
[ http://svm369.vetmed.lsu.edu/images/truman/Human%20and%20Armadillo%20Leprosy.pdf ]

I would suspect that pigeons are susceptible to most of the same diseases and parasites that chickens are. Sloppy gutting and incomplete cooking tends to be the basis of many of the bacterial/parasitical diseases from meat.

Shistosomaiasis is a tropical parasitical disease, and I don't believe it is found in the U.S..... today.

I saw squab on a menu once, and it did cause me to wonder if they had snares on the roof.

Sue