It appears I've started a "...Ever see poachers ____________..." (fill in the blank) trend on this forum!
Seriously, I really cannot remember seeing people take the blankets off the planes lately. I personally wouldn't want those reused from flight to flight rags with other people's germs on them. Being that the airlines have been cutting back on their availability, this might prompt such "poaching", especially if a pax has a connection, and is unsure whether the next flight will have any/enough blankets on it.
Usually when flying I do use a blanket only to cover my lap to shield against drink spillage from the pax next to me. I can't say how many spills on my trousers from other pax' drinks (or turbulence) those blankets have saved me from! Nonetheless, they never get near my face or other parts of my body, and I always wash my hands and/or use hand sanitizer after touching those blankets.
As I fly AA quite a bit, they offer nicer, clean (in plastic shrinkwrap) blankets in the premium cabins. I suspect those would be more sought-after loot by potential poachers.
Also, Air Canada now sells (I believe for $2) an inflatable pillow, with a disposable cloth cover, and a blanket inside it! Yes, a blanket. This is something you buy to take with you off the plane, not a rental item. They apparently don't have free blankets in coach anymore, but suspect they do in their premium cabins.
I bought one of these gizmos simply out of curiosity recently, and as one can imagine, the blanket is micro-thin and chintzy, but is clean, and works. I suspect the blanket would be torn to shreads if put in the washer, as they're nowhere near the quality of airline blankets we've been accustomed to. I wonder if any other carriers are doing similar?