I'm guessing you don't work in business. I'm a data scientist/analytics specialist so I'm well aware of how ROI analysis works.
If you're only looking at money in<->profits out you don't know anything about how your business works.
Businesses look at KPI aka "key performance indicators" https://en.wikipedia.org/wiki/Performance_indicator
These KPI's will tell you how well your business units are functioning is regards to the explicit goals of the company. You factor in their capital investment, staffing, etc to evaluate their value.
An ROI analysis does not look at happiness, etc.
KPI's can very well include customer happiness, especially for units involved in design. Because customer satisfaction = longer product usage = brand loyalty and repeat business. Those are all things that effect these units ROI to the company.
While I'm sure many government agencies exist without any clear connection to the value/costs they contribute/consume that doesn't mean it's a good way to run a government.