Chieftan: I've had a .357 Timberwolf for a little over ten years now. I have a couple of other .357 carbines (two Rossi '92 clones-16 1/2" & 20" bbl, and a Savage 24) but the little pump is my favorite.
Aside from its action, it has some other unique features. The butt stock is adjustable for "drop". You can set it up to fit you like a good shotgun so that when you bring it to your shoulder your eyes and the sights are perfectly aligned. You just focus on the target and squeeze - the can will dance or the rabbit will drop. Once it's set up for you, it's almost scary how quickly and easily you can hit small targets out to 50 yds.
The integral optics mount has appeal for some, as anything with Weaver-style rings will fit. Personally, I'd rather have the slicker receiver profile it'd have without it for ease of carry at the balance point and to make it possible to mount a good "peep" receiver sight. On the "plus"side, it's hell-for-rugged, you can't lose it, and it'll never come loose.
It weighs less than six pounds fully loaded with ten rounds, carry strap and swivels and is just 37 1/2" long.
With .38 Spl.s or mid-range .357 loads, it's a great small game carbine. The mild report seems to "spook" the other squirrels less than the crack of HV .22 LRs. I've never lost any game animal or varmint I've hit with it. With full .357 loads, coyotes and feral dogs out to about 80 yds. drop instantly with a solid shoulder hit. It'd do for deer with the right load at that range in a pinch, where legal.
For home defense, especially in a rural setting, it'd be a great choice with 125 gr. magnums, delivering significantly more of the "lightning bolt" effect that made that load the top stopper in police revolvers for many, many, years.
I think that IMI originally designed it for police use, and hoped to sell lots of them over here to LEAs as patrol carbines. They were a bit behind the curve, unfortunately, as the move to self-loaders as a duty sidearm was gathering momentum by the time it got here. It also had a design "flaw" which hampered it somewhat in "tactical" situations from an LEOs standpoint: the tube magazine can only be loaded with the action open. It might've been more widely considered if "tactical" reloads could've been done with the bolt in battery. For us civilians where the likelihood of a protracted firefight is slim, I don't think it's a big issue.
While I love my lever-actions, of whatever caliber, if I could have only one carbine the Timberwolf is the one I'd keep.