I have bad news for you...
3d Printing companies dont even recycle 3d prints / failures / waste filament all that well. It is cheaper for manufacturers to get raw product without the additives.
And if you mean just take the string straight from the racquet and feed it thru a printer, that wont work either, as the plastic needs to be 1.75mm diameter for most 3d print applications, and is a bit more helpful if continuous.