Re: "can we do it" --
The 4th amendment protects the right to be free against "unreasonable searches and seizures." Not all searches, not monitoring, not tracking. Unreasonable searches. To a lawyer (like 30-35 of 55 framers of the Constitution), "reasonable" is a signal to balance competing interests. That's what it signals now, that's what it signaled 200+ years ago when the Constitution was written.
So in the context of the 4th amendment, that is exactly the right argument to have. Whether a law enforcement tool is effective and necessary is a fundamental question you have to ask in balancing the competing interests of law enforcement and privacy. And that balancing is inherent in deciding whether a search is an "unreasonable" one.
Re: "should we do it -- it is self evident that a determination of whether a technique is effective and useful is instrumental in deciding whether we should use it.