Many private practice allergists don't take hospital call or consults.
Of course, at large academic institutions, allergists take consults. Common reasons for consults include drug allergy, pediatric/adult immunodeficiencies, eosinophilia, rashes (please call derm), anaphylaxis, HAE/urticaria/angioedema, or curbsides about our known clinic patients.
Plenty of stupid consults too...
Overall, when I'm on consults, it's not a bad rotation. I cover a very large hospital system. COVID has made it so we do lots of the consults as virtual/E-consults. I rarely get called after hours.