You are prompted to specify a location where your output feature class will be created. The location can either be a geodatabase or folder. The Output Location window does not show existing files because files are not valid locations for your output.
See the following for more information: Feature Class to Feature Class—Conversion toolbox | Documentation
Pro is intentionally only showing existing GDBs or folders in the Output Location window?
if so, why?
This creates extra steps (opening Windows Explorer to see all existing files) when exporting to other formats (like shp) besides GDBs or folders.