When flying I noticed that all the commercial aircraft I have been on use carpets as a floor covering. But why? If you fly in an older aircraft it looks worn out and it is susceptible to stains etc. Why do they not use one of the hard flooring options like linoleum?
The answer: High heels!
The local pressure of high heels would punch a hole in the aluminium or composite flooring, and a carpet is the lightest way to distribute the loads such that the local pressure from high heels can be tolerated. This is the real reason.
On the floor of the fuselage also very high localized loads can occur, especially from small-heeled shoes. Therefore floors need a strong upper surface to withstand high local stresses.
Other reasons are improved noise absorption and damping of vibrations. Nobody likes it when the floor panels start to resonate when excited by some engine or pump frequency.
With composite panels now in widespread use for cabin interiors, manufacturing flaws need to be covered, and carpets serve this purpose well. From Compositesworld.com:
Because sandwich panel facesheets are very thin, core print-through is common. Further, pinholes can form as phenolic resins outgas during reaction and cure. Therefore, panels visible to passengers typically are surfaced with some type of decorative material to cover surface flaws. Floor panels can be painted or covered with flame-retardant carpet.
Could you also imagine the difficulty of holding the trolley during turbulence or anything else? It would roll down and run someone over!
I also saw a Quora post where someone had pointed out it's also flame retardant, which is a good point.
Comfort is important too, not to mention another place to put advertising on some planes
Carpet is more pleasant
Aside from the practial reasons Greg already mentioned, most if not all people, will consider a carpet as a more pleasant material than ugly linolum. The fact that you have to replace a carpet after some years, counts also for most the interior in a plane (seats, board-entertainment, cover panels and so on). Furthermore a lot of people take their shoes of during long flights and a carpet feels in this situation a lot more comfortable.
In the good old days TWA rolled out a red carpet for their passengers at the check-in desk :)