My Canon F-1 with the mechanical shutter that goes from B to 1/2000 has instantaneous response. And, no, it is not as old as me.
It is only half as old as me.
The reason that there is a delay in shutter release is to accommodate the auto-focus feature. Since there is usually no by-pass of that feature in the point and shoot cameras, one must partially depress the shutter release button in anticipation of the subject arriving at the desired location for the photograph to activate the auto-focus feature of your camera. When the subject arrives at the designated spot, simply press the shutter release button the rest of the way for instantaneous response. It only took two tries for me to get the hang of it, so anybody can do it.
The only problem with this work-around is that you must find something to focus on that is the same distance from your camera as the subject will be when the photograph is made. Fortunately, this is not too difficult to do.
Happy photographing! Remember, good photographs are made, not taken.