That's the best use for a K-frame Magnum, and even S&W says ".38 Special for training, .357 for carry". If Bill Jordan says this too, who am I to argue

Jordan prompted S&W to come out with the k-frame .357 as the ultimate duty gun, since the only alternative at the time was the N-frames like the 27 and 28 which were heavy for all day carry.
I am a huge fan of the Model 10 and 64, but my Model 13 is basically what I consider a "Model 10 plus", the higher grade heat treating of the cylinder, barrel and yoke make these more durable than the 10's.
A few boxes of .357 in the 13 or other "K Magnums" won't hurt a bit, but I personally do not recommend a lot of .357's in them. Some say they shoot 158 gr. .357's regularly in them but I see no reason to do so.
I have a few Ruger Speed and Service Six revolvers chambered in .357 so I know how magnums handle in a medium frame revolver. I fired 18 158 gr. .357's in my 13 just to see how the particular gun fired with them, but I don't foresee any need I would have to fire any more.
The Ruger "Six" series are excellent k-frame sized revolvers, and use the same holsters and speed loaders as the S&W K frame. The Rugers can handle a lot more .357 though, and Ruger brought these out to take some of the LE market away from S&W as .357 medium frame duty guns became popular and police started to train with what they carried, which were 115-130 gr. .357's that started to break down their k-frame magnums.