You're somewhat mistaken. In the U.S., you aren't owed a warning that the cops are looking for you, especially if you're a flight risk. That was never part of it.
There are also valid reasons the other way, like consulting an attorney to challenge the warrant or prepare a defense before it gets executed, disrupts your life and prevents you from clearing your name because you're being incarcerated without bail. It's hard to investigate the charges against you from a cell.
Or the ability of journalists to inform the public of what the government is getting on with in their name. If the government is investigating their critics they have no right to keep it a secret.
That inconvenient bill of rights keeps us a step or two behind the rest of the anglosphere in decent to tyranny, but only for so long. It just takes a handful of dishonest judges to claim some right actually means something entirely different.
> Because in your eyes it is so gradual the difference between it's happening slowly and not happening at all is imperceptible and impossible to prove.
It's extremely straightforward to prove. You look at the laws that have been passed and the court opinions issued in the last 30-60 years.