Lets go over some of these cases. In almost, again almost, all of them there is a single theme. The police have seen a crime (abuse, fleeing suspect, evidence about to be destroyed). The emphasis on this is they have SEEN a crime being committed, about to be committed or have been committed. These are all viable reasons to detain an individual. Short of you witnessing a crime inside a private domicile, you have no right to enter. Even an anonymous call is not enough for you to enter without a warrant. If I call a cop on a neighbor saying he is currently beating the shit of out someone and you show up and actually SEE it, then we have a different story. However, if you show up, you don't see any abuse or violence, no one wants to open the door or talk to you, then you have to fuck off.
The issue with these cases becomes the police abuse of this clause, which happens more often than you think. The "we are here to ensure everyone is safe" is a blanket excuse to enter the premise without a warrant. It happened in the last link or perhaps all you need a suspicious bucket to enter. Perhaps they don't even need the excuse that someone is in danger and enter anyway. Continuing with the "anonymous tips" we have part 1 and part 2. Apparently your unconstitutional brethren in Las Vegas don't even need evidence to arrest a homeowner to [investigate the neighbor](www.youtube.com). Tell me, how is that last example legal? There are many potential, and historic, abuses of the "we are here for your protection, citizen" excuse.
Oh, continuing your excuse of "we have a duty to ensure the safety of everyone", lets look at Castle Rock v. Gonzales which states the police are NOT there to protect the citizens. So, what is your new excuse for "we need to ensure people's safety", which is a phrase for, we need to protect people?
Moving onto the destruction of evidence BS. What gives you the right to enter a home on that excuse? What cause did you have a person was going to destroy evidence? A gut feeling? A mere suspicion? The "evidence" is PRIVATE property until a warrant is issued for its seizure. If Bob has files, paper or digital, that the police want, and you think he is going to destroy them it is HIS property to destroy.
Again, the potential, and historical, abuse for this is huge.
What you people, and I use that term loosely to describe police, fail to realize is the 4th Amendment is very clear on warrants and seizures. Passing a law doesn't make it constitutional. If you want to enter my house without a warrant to ensure someone's safety, then join Congress, enter a bill to amend the Constitution, and get it ratified by 2/3 of the states.
As far as me being condescending, I have what is called the First Amendment. I could quote that one for you too, but there is also this which could help you out. I'm still looking for that pop up for you.