(TL;DR) While reading about preposition of on OED (eg avail of, enquire of), I encountered a possible explanation: quoted below, OED claims that the postverbal of originates from the genitive case, and from Old English. Would someone please explain? Or does a better explanation exist?
How did the genitive case (which concerns nouns) affect verbs, and produce this postverbal of?
Please expose, explain, and bridge all hidden, missing semantic drifts and links.
[Optional Reading] 39. In the construction of verbs.
a. After transitive verbs, the person or thing affected (‘secondary object’) is often introduced by of (representing an original genitive).
Such are balk, cheat, defraud, disappoint, frustrate; accuse, arrest, blame, convict, indict, suspect; possess, seize (a person of); avail, bethink (oneself of);
also with verbs with non-referential it as subject, as it repents me of;
and formerly with ask, beg, beseech, thank (a person of), etc.
b. In many verbal phrases, as
to have (also get) the advantage of ; to get (also have) the better of ; also formerly in to have compassion (also mercy) of ; to have (also take) pity of ; to keep watch of , demand or do justice of (= on), have the victory of (= over).
c. After intransitive verbs. Many of these in Old English took the genitive, and are found with of in Middle and Early Modern English, but this is now rare, except where of falls in sense under one of the branches already treated; instances are
to reck, repent, rue, beware (orig. be ware) of.
Verbs of sense, e.g. feel, smell, taste, touch (still with of in regional or colloquial use),
verbs of asking, as ask, beseech, demand, desire, entreat,
and others, e.g. distinguish, esteem, forget, like, seize, formerly construed with of, now take a simple object;
some, as accept, admit, allow, approve, conceive, recollect, remember,
still have both constructions;
with others, as hope, look, thirst, wait, etc.,
of has been displaced by for or some other preposition.