Right now DNA often comes in near the end of an investigation; you have to select people to test based on traditional detective work, and then you must legally acquire their DNA to match with your sample. If suspects don't want to give you DNA simply because you asked nicely, you have to be fairly sure of their guilt - and able to convince a judge of why you're sure - before you can get their DNA involuntarily. If this test became effective, the sample you got at the beginning would show you who among the likely suspects to test against, and probably lower the bar for getting legal clearance to take their DNA.
Not to mention you clearly have no clue how DNA testing really works; if it's important you can and will be able to match a decent sample to one and only one person. There are commonplace genetic tests that can produce 1 in 10 trillion profiles of a person's or sample's DNA to match against. The fact that this DNA processing produced a rough sketch matching X number of people is irrelevant when you'll be able to narrow that group to very few or one with the most basic detective work.