For generations (of Desktop versions), the "Feature to Point" tool had been limited to Advanced (ArcInfo) license level.
Users with lesser level were forced to use other methods to do the simple task of converting features to its Centroids.
Those methods included the usage of manual centroid Coordinates calculations, or python code (as suggested by ESRI), or 3rd party software.
For some reason, until now, there's no available Tool / Script Tool that addresses this issue (at least that I know of).
In this light, I've asked Mody Buchbinder to create a Script Tool that convert features to centroids, that will work with the Basic license level.
Mody had created the tool, which is attached to this post with its source python code.
The tool also include an option to use the "Centroid inside" which means that the point will be placed in/on the original feature.
The tool was built for Ver. 10.2.x.
You're all invited to use the tool and spread it.
Special Thanks to Mody Buchbinder for creating this tool.
P.S. I've recently published another useful tool that completes some lacks in the Basic license level: "Feature Vertices to Points for the people"