I agree that a K-frame Smith & Wesson with a 3 to 4 inch barrel is an excellent choice for a home defensive weapon, but we part company when it comes to using .357 Magnum ammunition because of over-penetration and recoil issues. Therefore I prefer the matching model 10 in .38 Special, and would also recommend that the hammer be bobbed and changed to double-action-only because thumb-cocking might be counter productive in a high stress situation.
The 13 is just a Model 10 that takes .357.
What makes the 13 perfect is that it takes the .38 fodder when it's in the home and takes the .357 when you're camping, hiking are on the road. The magnum ammo punches holes in vehicles, has excellent stopping power when you pull over at rest stops or are stalked by bears on the trail. Speaking of the latter, I recall hearing of a honeymooning couple that was stalked by a bear while hiking in the wilderness. The idiot husband left his wife, promising to return with help. His wife was subsequently attacked and partially eaten while her husband escaped without a scratch!
If she'd had a Model 13 stoked with hot magnum ammo, she could have lived to divorce her worthless husband or at least rethink her relationship! I wouldn't have trusted a Model 10.
So it's not that we're talking about .357 ammo in the home; we're talking about the ability to match the ammo to the threat. One could even load a 125gr JHP as the third round up. If the first two shots don't get an intruder's attention, the third shot definitely will!
Remember the 1986 FBI shootout in Miami? The bad guys were shot up with 9mm and .38 rounds, yet lived to kill two agents and wound five. All of the .357s used by the agents were loaded with +P ammo. Had the agents had 125gr JHP .357 ammo, the outcome very likely would have had a different outcome. (There were only two .357s used: a M19 and a M686. When I first read about the firefight, I saw that two .357s being used and found it incredible that they failed to stop the bad guys. It was only later that I found out they were using +P FBI loads, loads that had a fairly decent reputation.)
Three-fifty-sevens are only .357s when magnum rounds are used. The references to .357s in the Miami shootout were misleading at best. Anyway, when out on the trail or on the road, a .357 works much better than a .38 (regardless of the load).
Ruger and S&W both phased out their medium framed .357s for bigger and heavier versions. The Model 13 was a no-frills gun with no ejector lug and beautiful but nonfunctional wood grips. The barrel was perfectly balanced and the bluing was gorgeous. Plus the price was extremely reasonable. It was meant to be the perfect home defense weapon and I think S&W hit it right on the button.