The term evolved to from the combination of the prepositional phrase "Kath oles" (throughout all) and the word used for the organized, structured Church (ekklesia) such that by 109 AD when St. Ignatius used the term it needed no definition or explanation meaning that it was already well known and understood by the recipients of his letters.
(And for the record I betting there are a lot of things you haven't seen).
So is that your personal interpretation? The word catholic comes from katholikos and is never used in scripture. In fact, even the phrase "kath holēs" is only used in regards to multiple "churches" when it is used in regards to "churches". It's never used for a singular "church".