Indeed. This is like saying, “I’ve never heard/seen (famous comedy routine), but I read a transcript of it, and I don’t see what’s so great about it.”
Given that it’s readily available on YouTube you really have no excuse.
This thread would not be complete without Weird Al’s Harry Chapin-esque “The Biggest Ball of Twine in Minnesota.”
“Bitter Dregs” by Leonard Nimoy. 
“Sunday Mornin’ Comin’ Down”
“City of New Orleans”
“Boy Named Sue”
“Folsom Prison Blues”
all preferably by Johnny Cash.
“In the Ghetto”
“Cold Kentucky Rain”
by Elvis Presley.
“Ghost Riders in the Sky” by Johnny Cash.
Darcy Farrow. John Denver’s cover is the best.
It’s a Great Day To Whup Somebody’s Ass - Paul Thorn.
Peter Kagan and the Windby Makem and Clancy.
You can’t bloody get it in digital form or on CD, for some reason; only on tape or vinyl. As far as I can tell, you can get everything else Makem and Clancy ever did, which is pretty standard trad Irish music that you’d probably like if you’re into that…but this one song that’s in a whole different league, nooooo.
As noted by Tangent upthread, that’s originally a Robert Earl Keen song. If you like that one, he’s got a bunch of other great story songs.
By “Good Story Song”, do you mean the story has to be a good one, or can it be a crappy story but told well via song, like most of the hits of Red Sovine?
Me and My Uncle
It’s not an anti-war song really. More of an anti-establishment song, but mostly it is just funny in a wryly silly way. It is certainly a product of its time, but I doubt I or anyone else would be fond of it just for the storyline. Gotta listen to it.
A really short but poignant story: Norwegian Wood (This Bird Has Flown)
Two of my favorites:
Harper Valley PTA - Jeannie C. Riley
Pancho and Lefty - Willie Nelson and Merle Haggard
Yeah!
Also Famous Blue Raincoat by Leonard Cohen.
Frank Zappa “Let’s Make The Water Turn Black” a hilarious, disgusting true story.
The Ballad of Thunder Road
Brown Eyed Woman
Sloop John B
Lay down (Candles in the Rain)
Sink the Bismark (original spelling)
Lola
Just about anything by Chapin - we’ve hit Taxi, so I’ll go with the obvious - Sequel
The Highwayman - Loreena McKennitt
Master Charge - Albert Collins
I Got Some Outside Help I Don’t Need - BB King
And to be honest, just about every blues song ever written
Steve Earle has a ton of them. I recommend “Taneytown,” “Tom Ames’ Prayer,” and “The Week of Living Dangerously.”
Yes! He has so many good ones.
Athens Queen - bunch of guys loot a sunken ship
Flowers of Bermuda - captain gives all lifeboat seats away and dies on his ship
Barrett’s Privateers - pirating goes terribly wrong
Oh No, Not I - fooling around with some guy goes terribly wrong
A couple good ones from Steeleye Span:
Let Her Go Down
Gone to America