I started running games at conventions because, frankly, I was not having fun playing games at conventions. As egotistical as it may sound, I decided that if I ran games then at least 6 people plus me would get to have fun instead of no one.
Over time, I evolved into running "convention campaigns." That is, I run games that range for 3 to 6 four-hour sessions in length that tell a complete story. What I found was that some people who come to conventions do so because they don't have home groups, and a thing they found really fun and compelling was getting to enjoy a "campaign" over the course of a long weekend. Once I started doing that i realized I enjoyed a great benefit too: got to run a campaign I had been thinking about, but in truncated for, without the months or even years of investment. Sometimes I discovered that there was more "there" there and the con campaign extended from con to con. My longest was a Starfinder campaign that covered two conventions plus a long weekend, multi-session private game where half the folks were players from the con.
More generally: running games if fun. Running with strangers can be a challenge, but challenges are often fun. yes, it is possible to have a player that is very difficult. In that case, you have to use your grown up skills and solve the problem. But by and large, people that sign up to play a game with strangers are in and all they want is an enjoyable experience.