Evidence:
#1 How many other shows inspired engineers to actually try to build the tech?
#2 How many other SciFi shows inspired people to go into engineering school or to become a doctor?
Scotty's exploits as the Enterprise's redoubtable chief engineer inspired many students to pursue careers in engineering. Because of this, the Milwaukee School of Engineering presented Doohan with an honorary degree in engineering
#3 How many other shows have influenced the culture so that lines of dialog or plot points have entered the common culture? I can think of only one other show, the Lost in Space "Danger Will Robinson" line. I realize Dr. Who is a very long running and popular show, but I don't know of any lines of dialog or plots which have entered the culture from it. There is a drink called "Beam me up Scotty." What is the Dr. Who drink? Everyone in America can slip in "He's dead, Jim," or "beam me up" into a conversation and we will know what they are talking about.