does anyone know why sourd does not take avoir, as in avoir soif, avoir faim, etc?
"sourd(e)(s)" is an adjective meaning "deaf". There is a noun meaning "the deafness": "la surdité", but it would appear the French don't say "Ella a surdité" any more than we say "She has deafness".
It's only a guess, but I would say it's because it is a permanent condition, not a transitory one. One may be hungry, thirsty, hot, cold, xx years old, etc., and that will pass. But being deaf is not a temporary condition.