His name was Dr. David Viscott, who did an advice show out of KABC in Los Angeles. 

The producers went to watch his show in progress and came up with the ideas that become the hallmarks of the Emmy-winning comedy. And, as it turns out, it didn't just inspire one classic TV show, but two. 

"We went down to KABC here in Los Angeles and looked at — the guy's now since passed away — Dr. David Viscott. He used to be a radio psychologist here in the LA area and we watched his program."

Interestingly enough, [producer David] Lee claimed that Dr. Viscott was "really weird," though he didn't elaborate on why. The psychiatrist, who the Los Angeles Times dubbed one of the "pioneers of on-the-air counseling," began hosting his KABC talk show in 1980 and remained on-air until 1993, the year "Frasier" debuted.

Interestingly enough, during a DVD commentary track for the "Simpsons" episode "There's No Disgrace Like Home," Matt Groening revealed that Viscott was also partly the inspiration for the show's counselor character, Dr. Marvin Monroe."

Also fascinating to consider the creators originally wanted to have star Kelsey Grammer play a paralyzed millionaire - an idea the network nixed right away. You can only wonder what that show would have looked like. 

Frasier's Premise Came From An Unused Cheers Storyline & A Real-Life Radio Doctor