The problem is that the main true benefit of the information is to exclude people, but that isn't how people use it.
Suppose there are 2 million people in an area and you know some demographic information about the perpetrator that will allow 95% of them to be excluded. That is useful information.
But the probability that a random person in the relevant demographic is the perpetrator is now 0.001%. The demographic contains 100,000 people and one perpetrator.
The fallacy is in assuming that just because not being in the relevant demographic is enough to exclude you, that being in the relevant demographic should by itself be enough to suspect you.
That's still a much higher probability than 1/(2 000 000) so I am not sure what is your point there to use numbers.
"Oh, to catch the thief we are going to stop 100000 people" sounds absurd, after all.
Of course you can use the clue to exclude a bunch of people, but were you going to go around arresting random people on the street without this? Of course not, so why do it after.
There are more than enough documented cases of rape, assault and other crime in which the victim could not identify the perpetrator with any degree of certainty.
Profiling is an important tool in law enforcement but it works when it's built on proper evidence and statistical models not sketchy witness reports.
I skipped accuracy to observe that even correct profiling has problems, but it's hugely important to see that over-reliance on profiling is a threat to solving cases.
The memory and facial recognition stuff starts here http://lawcomic.net/guide/?p=3034
You hand-wave this part away too easily. It's precisely the reason that all protections in the legal system need to exist. If you hand-wave away uncertainty about facts, then there's no need to have warrants, reasonable suspicion, right to an attorney, trials, etc.
It's hard to construct a principled, narrow argument against profiling. If you have a single piece of exclusionary information, it's ludicrous to conduct a bunch of searches which are guaranteed to be worthless in the name of equality. (Leaving aside the accuracy of the tip for now.) And yet on a broader level, it's apparent that profiling can have all kinds of awful side effects.
An obvious example (and the metaphor carries) is secondary crimes discovered in the course of an investigation. There's another narrowly sensible rule: if a cop stops you for a broken taillight, they shouldn't have to ignore a corpse sitting in your passenger's seat. But combined with profiling, it produces a system where often-profiled people get the law enforced against them far more harshly than other groups. Add to that the cost and stigma of being investigated (a day in jail while innocent is a great way to lose a job), and you have a system where utterly sensible enforcement produces consistently biased harms.
The metaphor here carries really well. Imagine if those Kansas farmers torrented a bunch of movies, or that Seattle privacy advocate had a bit of marijuana. Well, those things are illegal, but it's still not fair that shoddy profiling amounts to selective enforcement against the profiled.
Even if you never, ever get incorrect data or wrongfully convict someone, profiling with limited data causes all kinds of secondary harms. This is a great non-racial example of why we should worry about it regardless of accuracy.