Clarinetists are well represented, so we have no reason to complain. According to my quick scan, they are the following, in the order they were inducted:
Benny Goodman (1957)
Sidney Bechet (1968)
Pee Wee Russell (1969)
Woody Herman (1976)
Johnny Dodds (1987)
Artie Shaw (1996)
Since the institution of the DB HoF, at least one clarinetist has been inducted every decade--until recently! That means we have to get mobilized, people. There are many clarinetists who deserve to be on this list, including Edmond Hall, Irving Fazola, Omer Simeon, and others. But for me the most glaring omission is Pete Fountain, who was the face of jazz clarinet to the public at large for several decades.
The sad fact is that many jazz fans, especially those born (like myself) after 1970, have never had the opportunity to hear a vast amount of the the great jazz Pete produced from 1959 through the '60s. Albums like The Blues, Live at the Bateau Lounge, Pete's Place, New Orleans after Midnight, and Pete Fountain Day have plenty of great jazz in them. In fact, they tend to highlight what few realize was the genius of Pete Fountain--an ability to take New Orleans jazz and blend it with other styles, moving it forward while inviting others in. Moreover, he helped revitalize the New Orleans jazz scene at a time when it was in danger of disappearing.
Too often great players receive their recognition after their deaths. Pete Fountain is still with us, though he is retired from playing. We have an opportunity.
I'm not sure how to get Pete "on the ballot" so to speak, but let's get this idea circulating, so that critics and fans alike will remember the contribution of one of jazz history's greatest showmen, and one of jazz clarinet's greatest innovators and virtuosos.