A paper entitled Promiscuous 2-Aminothiazoles (PrATs): A Frequent Hitting Scaffold appeared in J Med Chem recently DOI, in which they describe the promiscuous nature of 2-aminothiazoles in screens.
Exemplified by 4-phenylthiazol-2-amine being identified as a hit in 14/14 screens against a diverse range of protein targets, suggesting that this scaffold is a poor starting point for fragment-based drug discovery
I thought I'd check how often this substructure appears in the published fragments database, indeed currently 43 of the 903 published fragments contain this substructure. Further investigation identifies a total of 63 amino-substituted 5-membered heterocycles, and there are 167 fragments in which there is an amino group on an aromatic ring (mainly heterocycles).
It should also be noted however that there are 64 structures in the DrugBank database that also contain a 2-aminothiazole, so whilst promiscuous they can be developed into drugs.
So whether they are privileged structures or troublesome promiscuous hits is probably in the eye of the beholder, caveat emptor.