You are correct that a .357 mag. in the proper bullet weights does have the required muzzle energy at 50 yards to be used for legal deer hunting. But its not what I would call a good hunting caliber for deer sized or larger game. Just as the .223 Rem is legal in rifles its another caliber I would never recommend it for deer sized game.
Even though any kind of gun can kill a large game animal with correct bullet placement and a lot of luck (check out the link below to see what I mean).
Catfish Gumbo: Grandma's Griz
The ammunition is not designed for that purpose and causes as many wounded and crippled deer as it does kills because of improper bullet design and mass. The same with the .357 mag. it tends to over penetrate with heavy bullets due to less frontal surface area and most hand gun caliber hollow points are not able to reliably penetrate into the vital organs of large game due to rapid expansion.
This is just my two cents worth and I have been handloading over 30 different calibers for over 25 years.