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We can consider four aspects of your question:

Why do most events generate sound? What sounds get propagated? What does it take for sound to be detected? Has evolution got anything to do with this?

1 - generating sound Most of the sounds you describe are "broad band". Remember that a delta pulse (short sharp shock) is basically "all frequencies", although in reality a pulse of finite duration will not contain the very highest frequencies. Now it turns out (see for example my earlier answer on this topic) that it takes an absolutely TINY motion (less than an atom's width) to generate an audible sound pulse - so we can safely say "every motion makes a sound; most motions make audible sound".

2 - propagation of sound Like all finite-sized sources of energy, once you are a reasonable distance (reasonable compared to the size of the object generating the sound) away, sound intensity falls off as the inverse square of the distance (barring mechanisms to contain the direction of propagation: tunnels, mountains etc). This means that sound will typically remain audible for roughly the same distance as the object making it remains visible/interesting. Certain very loud sources (e.g. crickets) are an exception to this rule - but they are deliberately trying to be heard a long way off (see point 4). Sound is also attenuated by air - according to Stokes's Law, the attenuation coefficient $\alpha \propto \omega^2$, meaning that higher frequencies are absorbed more strongly (because of viscous interactions in the air). From the Bruell & Kjaer website:

Low frequencies really only get attenuated according to the inverse square law, but higher frequencies are attenuated more strongly.

3 - detecting sound In order to detect sound, a membrane needs to be moved. This motion then has to somehow be conveyed to the nervous system, which is water-based and therefore has a very different acoustic impedance than air ($z_0 = \rho c$ - so when density increases by 1000x and speed of sound by 4x, you have a mismatch...). The mechanisms in the ear (tympanic membrane, malleus, incus, stapes, oval window, cochlea) is a beautiful piece of engineering to create something of an acoustic match, and works quite well over a range of frequencies. Unfortunately, for very low or very high frequencies, bit of that mechanism stop working so well - the finite mass (inertia) of the components makes them more reluctant to move at high frequencies. This again puts an upper limit on the frequency we can hear. However, the "amplification" that the entire organ provides is exquisite - as I computed in the answer linked above this means you can hear tiny, tiny vibrations.

4 - evolution The human body is a wonderful machine, refined by aeons of evolution - "she who hears the approaching predator lives to procreate another day". The combination of "everything disturbs the air around it" and "we are designed to detect the slightest sound" is the answer to your question.