I was once on a team that maintained a SaaS application that was in some sort of bizarre super-position of "cost center" and "profit center" a few years back.
The company technically sold the app and made money from it, but they also tended to give it away almost for free as long as the buyer was going to be paying lots of money for the company's $FLAGSHIP_BUSINESS_SERVICE that integrated with the app. (Think of it like a free mobile game with micro-transactions.)
The primary way customers interacted with $FLAGSHIP_BUSINESS_SERVICE (and generated micro-transaction revenue) was through our application. However because the application wasn't what the customer was actually paying for, the executives had an impossible time deciding whether to treat the app like a cost or a profit center.
Whenever the app was working fine and everybody was happy the executives were convinced it was a cost center and looked down on it. Whenever it wasn't working fine and companies began to get angry and threaten to take their business elsewhere suddenly the executives would realize that without the SaaS application they wouldn't be able to sell more $FLAGSHIP_BUSINESS_SERVICE.
Long story short, it was a strange and frustrating experience in many ways.