It is however, not specifically the typical experience nor true for all individuals across the history of the nation, especially for significant portions of the population across a great deal of the nation's history, and it is remarkably less true for many in the nation at present.
The tools of oppression are globally available, and are in use to deprive people of those explicitly enumerated freedoms both within and outside of the US borders everyday.
That's just the way it is, and the way it has always been.
For specific cases past and present, see: Native American treatment and conditions at any point in time from the time of the Declaration of Independence and the Bill of Rights until this moment in time.
Also see the ongoing cases of extrajudicial incarceration and deaths at the hands of law enforcement officers of uncharged and non-hostile citizens and residents without legal repercussions from either state or federal judiciary.
So, no, one cannot count on fair trial nor the presumption of innocence in the US, even though that is very much the promised state of affairs. Wishing does not make it true.
The absolute number of "people detained" is meaningless, you have to compare it to the behavior of those people, otherwise you are led to silly conclusions such as that the criminal justice system fanatically hates men, because there are 10x more men in prison than women [1]. Once you normalize prison population by an indicator of violent crime, such as homicide rate, the USA stops being an outlier ('homicide' and 'incarceration' are rates per 100k) [2,3]:
homicide incarceration prisoners per homicide
USA 5.763 541 93.9
China 0.502 119 237.1
Norway 0.725 55 75.9
Canada 1.98 90 45.5
France 1.335 115 86.1
[2] https://en.wikipedia.org/wiki/List_of_countries_by_incarcera...
[3] https://en.wikipedia.org/wiki/List_of_countries_by_intention...
So in that respect, whites in the US are not so different from whites elsewhere.
[1] https://ucr.fbi.gov/crime-in-the-u.s/2019/crime-in-the-u.s.-... (I think due to incomplete reporting, and due to including only cases where some information about the offender is known, the absolute numbers do not reflect the number of homicides in the entire US, but it is still useful for relative comparisons)
[2] https://en.wikipedia.org/wiki/Demographics_of_the_United_Sta... (using 2020 numbers, which are close enough for the 2019 FBI stats, which are the most recent I know of)
It's 59% more.