I don't believe that we do have that right. I believe that the law says we do, but practically, cops have near-absolute authority to detain and arrest you, and you'd be hard-pressed to prevail in a civil case of unlawful arrest (and at that point, you've already been dragged down to the station, had your fingerprints uploaded to the Federal database, been strip-searched and spent time in a cell).
I also believe that upper-middle-class white males will have much more success in exercising that right than members of other societal groups will.
"...large gender gaps favoring women throughout the sentence length distribution (averaging over 60%), conditional on arrest offense, criminal history, and other pre-charge observables. Female arrestees are also significantly likelier to avoid charges and convictions entirely, and twice as likely to avoid incarceration if convicted."
I believe anyone that has obvious visible wealth can easily exercise that right -- police like that are bullies and only pick on those they know cannot defend themselves. If you take a upper-middle-class white man and dress him as if he were homeless, he will get the asshole treatment. Likewise p-diddy is renowned for talking shit to cops and having them meekly walk away many times in the past.
Not necessarily. I drive a Mercedes roadster. Several years ago I was pulled over by a cop who started ranting about how "rich people like you think they are above the law." I pushed back hard which the officer didn't appreciate so he told me he'd make it the job of his deputies to pull me over every day for the next week, which he delivered on. In fact, when I wanted to get somewhere in a reasonable amount of time I'd take the SUV. Of course because of his escalation of the issue I did walk away from my court date with a dismissal and the officer being quite literally restrained by his colleagues. So okay, maybe it helps but certainly doesn't prevent abusive behavior. There are many officers out there with economic chips on their shoulders.
I think that this is a misuse of 'right' in an important way. Rights are things that you have innately, not things that you are given; your rights can be abused or abrogated, but not taken away. Thinking of rights as things that are given to you, I believe, makes it easier on some subtle, even just linguistic, level to stop fighting for them when a purely philosophically committed person might fight on.
With that said, I agree that it is important to distinguish the practical consequences of exercising your rights from their philosophical consequences, though: while you should be able to behave in a lawful manner to police officers without fear of reprisal, it is important to realise that you probably can't.
Facing an angry police officer is one of the first examples in How to Win Friends and Influence People. I remember once where I turned the wrong way into a construction area late at night and accidentally drove on the tar. The officer was pissed at me and suspected I was drunk (I hadn't had a drop). Calmly explaining that I was tired and lost and had screwed up out of confusion rather than malice got me out of there with only a lecture.
Of course we have the right. The question is whether or not it is wise to exercise that right. In many (most?) cases, that would be an unwise choice, for the reasons you mentioned. And yes, that is problematic.
I believe it is important to understand that having a right, but choosing not to exercise it is a philosophically different scenario than not having the right in the first place.
I also believe that upper-middle-class white males will have much more success in exercising that right than members of other societal groups will.