Why do we need to replicate incomplete DNA fragments by PCR from a crime scene?
This process helps with the signal to noise ratio.  In theory, you could use the fingerprinting techniques to dice up the few billion copies of the DNA and carefully measure them.  However, it is far easier to replicate the DNA to increase the number of molecules of DNA available to the process.

Remember, fingerprinting for crime investigations doesn't involve reading the DNA, but merely uniquely identifying it.