Why do we say plenty of x?

Solution 1:

Questions about idiomatic usage are difficult to answer with assurance, but "plenty" came into English from the Old French, and likely the Normans used an "of" equivalent. They got the word from the Latin plenus, full, and nouns following that word take the genitive case.

Solution 2:

Probably a construction which dates back from its origins. The use without of is very informal.

Plenty (n.)

• mid-13c., "as much as one could desire," from Old French plentee, earlier plentet "abundance, profusion" (12c., Modern French dialectal plenté), from Latin plenitatem (nominative plenitas) "fullness," from plenus "complete, full" (see plenary). Meaning "condition of general abundance" is from late 14c. The colloquial adverb meaning "very much" is first attested 1842. Middle English had parallel formation plenteth, from the older Old French form of the word. (Etymonline)

Plenty of : (Usage note:)

• The construction plenty of is standard in all varieties of speech and writing: plenty of room in the shed. The use of plenty preceding a noun, without an intervening of, first appeared in the late 19th century: plenty room in the shed.It occurs today chiefly in informal speech. As an adverb, a use first recorded in the mid-19th century, plenty is also informal and is found chiefly in speech or written representations of speech.

(Random House Dictionary)

Solution 3:

Plenty in ME was (at first) not an adjective but a noun, meaning "fullness, abundance". When conjoined with another noun, it would take 'of' in its partitive genitive sense, e.g. plenty of time, as we today would say "with an abundance of caution".