This is a very glib take. The origin of the series was a 1985 educational computer game from Broderbund. The target age group wasn't expected to know all this information, which is why the game shipped with an almanac.
“The show was created partially in response to the results of a National Geographic survey indicating little knowledge of geography among some of the American populace, with one in four being unable to locate the Soviet Union or the Pacific Ocean.”
https://en.m.wikipedia.org/wiki/Where_in_the_World_Is_Carmen...
Now of course the tv show is an offspring from the video game but it’s well documented that the specific format was to combat geography. So it’s a fine statement to state that is the purpose of the show creators as that was the mission from PBS at the time.
Was there a show? To me Where in the World is Carmen Sandiego was a reoccurring segment on a show called Square One. I liked it, but it didn't feel like it was the source of Carmen Sandiego mythology; it felt more like a minor epiphenomenon.
There was also a computer game, which I didn't play much of because it was a lot of work. It felt a lot more fully developed than the TV segments, though.
0: https://en.wikipedia.org/wiki/Where_in_the_World_Is_Carmen_S...