What is the history of FOIL? and why does it seem to be emphasized over more general methods of multiplication (like use of the distributive property or tabular multiplication)?
it is required to multiply binomials.
FOIL method has been around as long as Algebra although it may have had other names, it is emphasized because although the order doesn't matter, it is required to multiply binomials. FOIL, in fact is an extension the distributive property, you are distributing one binomials over another and although you can multiply binomials with tabular multiplication you are really doing the same thing as when you FOIL.
The actual term fist appears in William Betz's 1929 high school algebra text, it was a meme to help math students remember how to multiply binomials.