The problem is: 50% of the population is of below average intelligence (by definition, if you take 'average' as 'mean'). Most of that half of the population, although sufficiently intelligent to be employable are barely numerate without electronic assistance (or for the older generation pencil and paper). On good day they can make change or check their change! A significant subset of them are generally incapable of operating technology except by rote memorisation of the operating procedure and regard any variation of that procedure with great suspicion or even refuse to accept it.
The proportion of the population that can calculate a trapdoor function in their heads, without muttering or writing anything down, is vanishingly small and probably almost entirely composed of above average MENSA members.
Therefore, authentication by unassisted secure key exchange is almost entirely outside the capabilities of the human population of this planet..
The only remaining possibility is the use of a one-time pad. It is only secure if the pad is, so that would require the human user to memorise and destroy the pad, which would be unique to that user. Unfortunately in a secular, post Gutenberg* society, the accurate transmission of large texts (e.g. epic sagas) by rote memorisation and oral recitation is no longer generally valued, so those few with the aptitude required rarely discover and develop their memorisation skills.
* Gutenberg: the 15th century German printer, not the 20th century book archive.