We know this for sure since there is an extremely rare disease in which people literally feel no pain. These people have a very tough life, and have to constantly manually inspect their bodies to make sure they don't have injuries they're not aware of (cuts, sprained ankles etc.), and are also essentially unable to participate in any kind of sports because of this.
For example, when putting your hand on a surface, if you didn't feel the pain of extreme heat, you wouldn't know that your skin is getting burned. Or, if you miss-stepped and sprained your ankle but didn't feel the pain, you would keep putting your full weight on that sprained ankle and probably turn it into a serious injury. Without pain, you wouldn't know you're having a heart attack and wouldn't seek any medical attention. I can go on and on: accute pain is extremely important to basic health. You can't "be careful", unless you think it's reasonable to get full medical checkups after every walk.
Note that "acute" means "short lived", it doesn't mean it's particularly strong. It's the opposite of "chronic", which means "long term". For example, when you prick your finger, you're feeling some (very mild) accute pain, which serves the purpose of letting you know your skin was pierced and you need to stop pushing in that direction.
My whole point was that this is utterly wrong, and that, while stress during a traumatic experience is normal and potentially even required (akin to pain), stress after the experience is definitely not a good thing, and should be treated in any way possible (whether that's family support, therapy, or medication is up to every individual case) - just like chronic pain.
Relating to pain, people should get relief as soon as the pain has done its job - that is, as soon as they know about the injury and the area they have to protect - any more pain than that is unnecessary, even if normal. In the vast majority of circumstances, I imagine this is probably a matter of seconds or minutes after the injury occurred. I can imagine some weird, vanishingly rare, circumstances where the pain may legitimately need to be endured for longer, but that would be splitting hairs.
And an accute anxiety attack (assuming this occurs without some traumatic event) is obviously not normal or helpful and should be treated immediately. If this anxiety attack is happening during a traumatic event (say, I am currently being held at gunpoint), taking a pill to calm down may be less required (though even that is debatable, especially for a panic attack, which generally leaves you entirely helpless).
When has grief done its job? I've never been held at gunpoint yet somehow experienced stress on many occasions. How many of those do you want to subject me to? The DSM generally says 6 months to become a disorder for most things from what I've read. How about considering a question that isn't trivial to answer?