A bit speculative as this seems to be, given current attitudes in most societies towards nudity, this would be a somewhat promising scenario.
All human infesting lice species are parasites that depend not only on skin contact for nutrition but on certain types of fibres to dwell, to hide, to travel and to procreate. Eradicating this natural habitat on a large scale is very likely too destructive and radical for the lice to adapt quickly enough to such a new situation.
But there is also a problem:
Apes, lice and prehistory (2009)
Head and body lice used to be designated Pediculus capitis and P. corporis but they are now known to belong to the same species, P. humanus x. Fifty years ago Levene and Dobzhansky showed that head lice could be trained or adapted to become the rather larger body lice by attaching them to the body in small pill boxes.
More extensive phylogenetic analyses [16,17] indicate that body lice evolved from head lice several times within the worldwide clade A, as they are found in many branches of the cladisitic tree. Multiple derivations of body lice from head lice had already been considered by Zinsser 1, and it makes good sense if one considers that clothing was not a single invention. Wearing animal pelts fur-side next to the skin would have provided a suitable place for lice to breed before fabrics were developed with the inventions of spinning and weaving.
In 17th and 18th century Europe, most of the aristocracy and gentry shaved their hair and wore wigs. Had this custom arisen to protect them from lice as Zinsser suggests? Not according to Samuel Pepys' diary, as he complained more than once about his wig being infested: "Thence to my barbers, to have my periwig cleared of its nits." I wonder if they were head or body lice – is a wig hair or clothing?
Lice and nudity
Why naked apes are naked and when we 'lost' our hair has long been disputed, as discussed by Desmond Morris in The Naked Ape. Rantala suggested that nakedness could have had a selective advantage to rid the body of lice and other ectoparasites, a view also championed by Pagel and Bodmer, who added that being seen to be free of lice would be a fitness indicator and a good mating strategy.
These little parasites are highly adaptable and while not that robust in general, the amount of fibre, fabric or hair they need to breed is really minimal.
Shaving can be safer head lice treatment than insecticides (2005)
Sladden and Johnson reviewed common skin infections in children.1 The life cycle of head lice (Pediculosis capitis) was well described and is similar to that of pubic lice. I worked in chronic emergencies in Somalia in 1993 and Sudan 1996-7 among internally displaced populations and in the nomadic Karimajong of Uganda in 1998-9, whose poor hygiene would have been a good breeding ground for head lice. However, head lice were never a clinical problem because these populations know how to interrupt its lifecycle: they shave off their hair, the only place where the eggs (nits) are anchored and glued close to the skin. Lice outside the hair are not transmissible and do not cause infestation.
It is therefore likely that we might be able to not only reduce the lice problem, but to eradicate them completely. But only by going naked and really
Pubic lice: an endangered species? (2014)
The incidence of pubic lice infestations is estimated to be between 1.3% and 4.6%, with an average incidence of 2% worldwide. It is also estimated that 70% to 80% of adults now remove pubic hair in part or entirety, using a variety of methods. It is hypothesized that the destruction of this pubic hair habitat may account for the falling incidence of pubic lice and may possibly lead to its eradication or atypical presentation.
Aim: To report the changing incidence of pubic lice infestation from our unit over the last 10 years and assess its association, if any, with pubic hair removal of any kind.
Methods: Assessment of medical records and questionnaires were used to identify the incidence of hair removal and pubic lice infestation over a 10-year period. Data were anonymized and analyzed to identify any correlation.
Results: A significant and strong correlation between the falling incidence of pubic lice infections and increase in pubic hair removal was observed, with a Pearson correlation r value of 0.9686 (95% confidence intervals, 0.88-0.992). The P value is less than 0.0001.
Conclusions: The increased incidence of hair removal may lead to atypical patterns of pubic lice infestations or its complete eradication as the natural habitat of this parasite is destroyed.
That seems to be the future. Well, a possible one. Prudes then need to find something else to get their pulses up.