Wikidata about the text used on properties. The idea is that the label used is fixed. My understanding is that as a consequence once a property is given a label, it remains that label always and, there is no way to change it both in Wikipedia and Wikipedia.
Best practise at Wikipedia is that you can override text as the editor sees fit. For instance: P570 has a label of "Date of death", when it is used in a template for people who were executed, an editor may choose to use "Date of execution" instead.
When you consider that there are over 280 languages with a Wikipedia, the notion that both the labels and its aliases in a language are unique has been demonstrated to be problematic. In addition there are Wikipedias without labels in that language. Once people start adding labels, it is not obvious that the first label chosen is correct. It is obvious that the property will not be recreated because someone made a booboo.
In conclusion, it is best when properties can be selected based on a label and a description. Internally the property identifier is used and the label is provided as a default for use in Wikipedia. In this way there are no problem for editors. The only issue left is that some developers have to scratch their head on how to do this.