“Houston” “Cougars” chant has been tried before and failed to connect with the fans. It was UH’s version of “Texas” “Fight”. A cheerleader would get on one side of the field and hold up a sign “Houston”, and the other cheerleader would stand on the other side of the field and hold up a sign “Cougars”. Just like the UT cheerleaders do for Texas Fight.
I think its more about the UH fan base. Side-to-side chants haven’t worked in Houston.