"Who cares"? You care. You are shooting at a swarm of bees of known number density n and depth d (the foil thickness) trying to infer the size (surface area) of each combined with your pellet, σ, from the number of hits! I assume you want intuition on WP or your modern physics text.
Assume you are shooting at a swarm of bees of a given unknown size/radius a with pellets of size b, and you wish to determine the unknown bee-pellet cross-section
$$
\sigma=\pi (a+b)^2,
$$
a fundamental property of bees & pellets. The swarm is very sparse, say with $n= 1/m^3$, and has thickness/depth $d= 10m$; and, moreover, you can detect the kill ratio (probability of interaction), say from the number of smeared pellets recovered.
For $a+b= 10^{-2} m$, your pellet sweeps a cylinder of volume σd through the swarm, so it encounters dσn~ π/1000 bees. Thus, from this kill ratio, you may determine σ, a fundamental quantity related to the size of bees and pellets, never having examined a bee closely. If you double the thickness of the swarm, you double your kill ratio.
How far will that [pellet] go inside the [swarm] before hitting [a bee]?
Note for an almost certain kill, on average, you'll need a huge depth, d~λ=10 km/π. Whether you choose to parameterize your kill ratio by d/λ is optional, but why not work in the units of the small object you are investigating, in this case the bees (cum-pellet)? You are not studying the swarm (whose bee density your know): you are studying the bee size. In HEP, people investigate femtobarns, $fb= 10^{-43}m^2$, so they investigate distances of the order of millionths of a fermi.
