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You are right that the concept of privacy is relatively recent, but imho it has little to do with the communal vs. solitary performance of everyday tasks. Different social groups use different technologies and machinery in very different ways, which are socially defined. The Amish of Pennsylvania avoid technologies which they see as undermining the social cohesion of their community, but do not avoid technologies in general. Thus, they avoid automobiles (because they give individuals freedom of movement) but not buses or trains, electricity (because wires "connect" them to the outside world) but use instead propane powered household appliances. In Eastern Europe, mechanical laundry and pressing services became a social institution similar to Irish pub - where women would gather, socialize, and exchange news and gossip. Likewise, movie theaters in the US are institutions of communal viewing as opposed to individual viewing at home. These cases demonstrate that every technology - transportation, laundry, or cinematography - can be consumed either collectively or individually or both, and that depends on the accepted "uses and gratifications" in a particular social setting.
As to doing my laundry at home or in public laundry - I've done both. Doing it home is much more convenient and less expensive in a long run. The cost of a single wash load in coin operated laundries in the Baltimore area is about $1.50 - $3.00 depending on the size and location. Drying it in a dryer cost additional $1-$2. One can buy a washer and a dryer set for about $450 new and about $150 used which pays for itself after 150 or 50 loads. Not to mention the fact that my own washer and dryer gives me a much greater flexibility over public laundromats.
Wojtek