This type of discussion is common.
Can the .357 be used for deer hunting? Yes,,, it can.
Is it the best choice? That depends.
In general,,, other calibers will perform better, when a margin of error is desired.
A proper bullet design, combined with a proper bullet placement,, it can be a fine deer hunting tool.
But we are dealing with flesh, blood & bone. Combined with an animals desire to live, and all the dynamics that go along with that.
A deer has a "thin" skin when compared to many other critters. And the muscle mass is larger than some, and smaller than others. Combined with bone structure,, again, it's a subjective subject.
As a Hunter Safety Instructor,,, I teach "Ethics" as part of the class. I also teach a bit of anatomy so people know what is necessary to humanely kill a deer with one clean shot.
And I also say; "But NOTHING is a guarantee, even if you do it all right."
A .357 is often touted as a great SD caliber,, when combined with a 125 grn JHP or a JSP bullet. A human body is DIFFERENT than a deer.
Most folks agree on a few things necessary for a clean, one shot quick kill when hunting.
Complete penetration.
Quick death causing damage to internal organs.
And if bone is encountered when it's shot,, the bone must be broken to where the bullet can continue on the proper angle to cause such damage.
Basically we are asking a lot out of such a small item.
The angle of the bullet path. The ability of it to do all that's necessary w/o fail. And the reaction of the deer to it's injuries.
I prefer a good quality hand cast bullet for revolver hunting. I match the bullet to the game & what I hope will be a well placed shot. Ideally, the bullet is able to enter a spot where it doesn't encounter any bone (between ribs for example,) hits the lungs and heart, and exits with a big enough hole to allow for quick blood loss.
Ideally.
Now, reality. Often, a bone is hit as a bullet enters, and as it exits. Ribs, shoulder blade, leg bone all MAY be impacted during entry. And the same is true for when it exits.
The bullet needs to be hard enough to completely penetrate all that,, AND exit with a large enough hole.
And it's desirable to have the bullet nose soft enough to where it expands some,,, without coming apart, to cause more internal damage.
So, with all this,, it's fairly impossible to have one bullet to be a perfect choice for all variables. And that's not just for the .357.
A good medium hard cast solid, or even a good medium hard HP design is often a good compromise. But a good jacketed bullet of the SP design is also a good choice. Often, the JHP's seem to be more prone to separation & less penetration IN GENERAL,, so many shy away from those. Yet,, MANY deer have been killed with a good quality JHP bullet as well. It's often the bullet placement, combined with the choice of which JHP is used.
So what's the best answer?
A quality accurate bullet in your gun, with a proper bullet placement, can & will be a good deer killing combination. But only you, with the ethics to PASS on a shot, that might be marginal can determine what's "best." And that's not just in .357,, that's ALL calibers.