Let's say 1% of the population commits crimes.
Let's also, for the sake of argument, say all crimes are committed by black people.
Of the general population, 10% is black.
If you profile all black people, you will indeed profile the 1% of the population that commits crimes, but you will also profile 9% of the population that does not commit crimes.
And before you say "not the entirety of the 10% black population is profiled": maybe ask some black people about this. It's not 100% of the black population that gets profiled but certainly a very significant percentage.
And even if it's just half or even a quarter of the black population that you're profiling, you're still profiling a lot of innocent people.
This is the reason why profiling is bad.
(and note that in reality the figures are even worse).
If there are credible reports of a white man committing murders it doesn't make any sense to waste resources listing mainly female Asian suspects, for example. There are also other similar issues. For example, if a crime happens on my street I expect to be treated as more of a suspect based only on my proximity.
The issue of racism is (and needs to be) grounded in things other than rational resource allocation.
However, it's clear that the vast majority of resources are devoted to black areas and poor areas, and to responding to directly "violent" crime. A mugging is more sensational than white collar crime, but from a purely utilitarian standpoint, I'm not sure it's rational to devote more resources to catching the mugger when, for example, there is widespread wage theft depressing incomes in the mugger's city. Which causes more damage in the long run?
If all crime is committed by South Asian women, you're right that it would be madness not to use that information to target crime-fighting measures such as, for example, only looking for suspects that are female and have a South Asian suspects.
Profiling, however, where you preventively search if not outright harass people, is something entirely different: if one in ten South Asian women engage in crime, every time you preventively search and harass one of them, you have a ninety percent chance of searching and harassing someone who is innocent.