Carpet in a walkway fails in two ways at once. Soil works down into the fibers where a vacuum cannot reach it, and the fibers themselves get crushed and abraded until they scatter light differently than the carpet around them.
The first problem is solvable. Hot-water extraction flushes embedded soil out of the pile, and pre-treating the lane before extraction gives the cleaner time to break the bond rather than just wetting it. Most grey lanes lift substantially.
The second problem is not. Once the fiber tips are worn and split, the lane will always read slightly different in raking light, no matter how clean it is. Any company that promises otherwise is selling you a disappointment.
Pet accidents are a separate category. Odor lives in the pad and subfloor underneath, not only in the carpet, so surface cleaning masks it for a week and then it returns. Treating it properly means getting to what is underneath.
Between professional cleanings, the highest-value habit is simply vacuuming the walkways more often than the rest of the room. Most soil is tracked in from outside and does its damage in the first few feet past every door.