What does the default have to do with it? We are already not in the default situation. Interacting with police at all is not the default! If you mean to say something like "it's not likely" or "they're not doing it in unreasonable cases" then your anecdote is not relevant.

> And why would someone threatening people with a knife deserve benefit of the doubt?

Several reasons, which would be obvious if you tried to think of them. Most knife-wielding maniacs are, well, maniacs, and aren't fully in control of their actions. Innocent bystanders are regularly killed by police discharging guns accidentally or inappropriately (in fact, even police are frequently killed this way). People are routinely misidentified by police as carrying weapons when they aren't. Police often give misleading or unclear instructions while trying to de-escalate, and with a gun drawn, failure to comply can and does result in the suspect being shot.

Bear in mind that what you are excusing is essentially a (substantially increased likelihood of) extrajudicial execution. It should be a last resort. It's not enough to say "well he's clearly a bad guy, why give him the benefit of the doubt?".