I've always believed in using a tool for it's proper task. I don't typically drive screws with a hammer or drive nails with a screwdriver.
To me, that's what taking a bike like the Versys, V-Strom, Ulysses, GS, Tiger, Multistrada, etc. down a single track trail, up steep hills, or over big obstacles like.
Riding down an improved gravel road is something any motorcycle can do. Even sportbikes can navigate some pretty gnarly roads as seen here:
Anyone who watched the show "Long Way Round" which featured Ewen McGregor and Charlie Boorman circumnavigating the world on hulking BMW GSes will remember that Claudio, their camera man, ended up on a cheap, lightweight POS bike when his BMW broke down. He was able to maneuver much easier and cross obstacles the big GSes couldn't due to their weight.
Biggest bike I would ever want to ever take in the soup is a KLR. I tried it once, and got stuck. Had to drag that sucker out by myself. Even that bike is pretty dang heavy.
19" front wheel or not, a 400+lb bike is a heavy beast in the deep stuff. A 500lb bike is past the point of fun (unless you like destroying your motorcycle).
Now, piloting a trials bike over big logs and such is a great deal of fun. Drop it, pick it up, keep going.