At most schools, what you are describing are called “club sports”. These sports have much less funding from the university, and they are ubiquitous.
The next logical question is probably “why aren’t all sports club sports?” The short answer is that varsity football and basketball are often direct or indirect money makers for the school that warrant funding for competitiveness, and title ix that says that there has to be access to sports at equal levels (typically this means a university needs a few women’s sports that have equivalent quality equipment, facilities, etc. as football and basketball).