Is it a valid approach to modify an analytics builder model programmatically using APIs in order to add for example new measurement inputs for new workers in this model? I am trying to think how API would help in doing it vs. doing it manually in the web interface
there is no public API to do that and the structure of the underlying model may change so I would not recommend it. Have you looked at using template variables for the workers and then using the instance editor to add additional instances for new workers?