Abstract expressionism began roughly in 1946, and the whole stance of the ab-exers was, among other things, that America had no art. Sure, it had a lot of Romantic and Neo-classicist, and Art Deco influences, but those were all European. The US didn't go through its own modernist Avant-Garde in the sense that Italy, Germany or Russia did, and the best examples from previous decades were all to social-oriented for the late modernist liking.

And so the abstract expressionists intended to start their own traditions as opposed to merely adhering to the existing European ones, thus, among other things, also creating the first uniquely American art. The time was right and the ground was good, since a huge wave of emigration before and after the war brought a lot of new influences into the US art scene as well. So in turn, while many of ab-exres did, of course, still borrow heavily from the European experience – Newman, notably, was much inspired by Malevich and Mondrian – the end result was something rather convincing.

The factors above also contributed to the rise of American collectors – people like Leo Castelli and Peggy Guggenheim, whose patronage provided the artists with the means to work more or less full-time.

As a result, abstract expressionism became the first primarily American art movement that got a huge following internationally – lots of late modernist movements later emerged in Japan and Korea in the following decades. It also notably shifted the balance of cultural influence in the arts, and what later served as great base for later movements, most notably pop-art, land art, conceptualists, etc.

But, and that'll have to be put in rather ahistorical terms, but it can not be overstated – the major reason any art movement takes hold is when people there make damn good art. This does not historically correlate with anything, honestly – some emerge in social upheaval, some in degradation, some in extreme multiculturalism, some in isolation. There are likely no patters there whatsoever, except maybe that some people get lucky with meeting great peers. Who knows.

At the end of the day, abstract expressionists made great stuff, and other groups made stuff that wasn't as great. The reason why that happened is, again, not a history question – it happens entirely within the confounds of the art discourse that I won't get into here unless anyone is specifically interested, because that would inevitably lead to a Great Wall of Text.

Some sources:

Art Since 1900: Modernism, Antimodernism, Postmodernism

Daniel Belgrad, The Culture of Spontaneity. Improvisation and the Arts in Postwar America

Dave Hickey, "Air Guitar: Essays on Art and Democracy"

Serge Guilbaut, How New York Stole the Idea of Modern Art

Marika Herskovic, American Abstract and Figurative Expressionism Style Is Timely Art Is Timeless

Jackson Pollock: Key Interviews, Articles and Reviews

David Anfam, Abstract Expressionism