Chesterton isn't for everybody.
"All I got from that tome [Orthodoxy] was that Chesterton is enthralled by-- even distracted by-- the sound of his own words; his tangents are intolerable." Thus wrote a friend of mine some years back, reminding me of a bad habit--responding to a philosophical question not with an answer, but with a reach back to my book shelf with "here, read this."
I still enjoy Chesterton, but if someone asked me the same question today, i.e., what the hell is the point? Why go to church or give a hoot what organized religion has to say about anything, then I don't think he'd be the first writer I'd think of. His once captivating reliance on paradox seems to me now ...to pall, to be too clever. And dated. The rhetorical tool of a writer who doesn't have the time to stop and perhaps read a little more about the issue at hand before writing.
To the extent that this mode of writing persists (especially among conservative journalists) illustrates the degree to which Chesterton's influence has been problematic. A century after his most celebrated works, we know so much more about evolution, cosmology, history, etc., and yet too many pop conservative writers content themselves with knowing no more about these issues than he did at the time.