OK, now that I have several models, it seems that in order to run an entire model, I have to go and edit it, and use the Model menu to run the entire model. Does modelbuilder let you make executable scripts that simply run on double click, but are editable with right click? ArcGIS Desktop 10.4 here.
You mean you want a user interface for the model? If you set up some parameters and manage them under Model > Model Properties > Parameters, when double click on the model that you built, there will a user interface similar to other existing toolbox.