When P&G was still battling to get housewives hooked on Tide and away from soap for washday, some bright blub in marketing came up with the "no rinsing" required concept.
As we all know laundry washed in soap must be rinsed at least thrice or at best twice. Otherwise all dirt, suds and other residue wouldn't be removed and one ended up with "tattle-tale" grey laundry.
Tide being a synthetic detergent didn't have the same issues as soap on wash day, so *someone* concluded things didn't need to be rinsed.
Adverts one has seen for this "no rinse" Tide seemed always to target wringer washer owners. That may have been because unlike those with fully automatic washing machines owners of such semi-automatics still were tied to rinse tubs and doing multiples of that process.
When you consider how high sudsing Tide detergent was then (and until rather recently for that matter) one wonders if even one rinse would have been enough.