It's been written that The Cowsills turned down the TV show offer because Shirley Jones was to star as the mother. The Cowsill family collectively declined the offer. They wanted their own mother to play their mother.
They certainly had the looks and talent for their own TV show. They were immensely popular at the time and their four and five part harmonies were flawless.
They were humble too. I remember taking my sister to a local department store where The Cowsills were doing a record-signing. My sister struck up a conversation with Susan that went on for over twenty minutes. They were good friends by the time I had to take my sister home. They were all genuinely friendly to all their fans that day.