The whole assuming humans to be rational part is what messes up the calculation.

But now I feel stupid for writing this.

Don't stop now, keep going and you'll be writing financial regulations in no time!

The mistake is in thinking people would only pay money for things they will enjoy. This is self reinforcing; people will believe they enjoyed something more if they have been told it is more expensive. What if that's a false belief? What if the economists were paying each other purely out of spite and enjoyed nothing? Desire and pleasure are separate and it's possible to have the former fulfilled with none of the latter.

Assuming humans to be rational, it could be argued that there was a net gain of utility (if 100 $ is worth more than what you lose from eating excrement) or at least remained the same, since the buyers considered the entertainment they get to be worth at least 100 $ and that the service providers considered their service to be worth less than 100 $).

Counterpoint: If humans were rational, they would not find it entertaining to watch people eat excrement.

I kind of thought that was the point of this. There are many ways to increase GDP or gain 'utility' through how we use our money, but most of it is just shit. Capitalism values anything that can do this regardless of any other sense of value.