As another comment correctly pointed out, hyperventilation lowers your blood CO2 levels below normal/healthy thresholds, and the intent of paper bag rebreathing is to slow your breathing, and have you breathe in less oxygen-rich air/previously exhaled CO2. While the mechanism of:

>hyperventilation -> low blood CO2 -> increase blood CO2 -> alleviate hyperventilation

is well accepted, I don't believe that there is robust science supporting paper bag rebreathing specifically.

Additionally, paper bag rebreathing can kill people who are sensitive to hypoxia (lack of/low oxygen) and people who are suffering medical emergencies that appear like anxiety attacks but aren't (commonly heat attacks). AFAIK, the current recommendation is to coach people through their breathing, and to have them breath through pursed lips. While paper bag rebreathing should be fine for otherwise healthy people, there's not really a reason to use a method that could be dangerous when there are less/non-dangerous methods available.