You missed the parts about "unreasonable" and "without due process of law".
Reasonable suspicion has met the constitutionality requirement. In Terry v. Ohio, 392 U.S. 1 (1968), SCOTUS said that a brief detention under reasonable suspicion, including a frisk for weapons, meets constitutional requirements.
In Hiibel v. Sixth Judicial District Court of Nevada, 542 U.S. 177 (2004), the SCOTUS also found that requiring identification met the 4th and 5th Amendment requirements.
The power of the police to stop, question, and frisk under reasonable suspicion is something goes back to our Founding and before, as a part of English Common Law. It's a very recent liberal view that questions it.
But that begs the question of what is reasonable suspicion?
What made you suspect that person? What is the reason?
That they live in a bad neighborhood?
Their skin color?
They were walking? ...walking too fast? ... walking too slow? ...in a hurry? ...waiting for someone?
They were pulled over for a burned out license plate light?
What is the
reasonable suspicion that they, in fact, have anything on their person or in their vehicle which is illegal?
The reason 'stop and frisk' was shot down in New York is that the only reason necessary was that they were there.
I'm no fan of criminals, but I have lost too many rights to the Drug War being executed with (over) enthusiasm, including civil forfeiture. If I have a nice watch are the police going to take it? If I carry cash is that a goner? We have already seen this with vehicle stops and airport searches, and now do we want it on the streets?
Who is guarding the guards?