Does the account you are logged in with when you see blank values for the lookup field in the SharePoint list have access to the SharePoint list hosting the lookup field? If not, the entries in the lookup field will be blank. This is one possibility.
This is a lookup field that stores the selected value as a JSON object in a text field, not the SharePoint lookup field that is a foreign key to another list.
I did just as you describe. I had the control create the "Save to" field and add it to the view, but when I look at the view it doesn't display anything. I finally added the following code to format it: