Is there any benefit to mixing bread dough by hand?

You can achieve great results by hand or using a machine, it's a matter of technique. I prefer kneading by hand as it has the advantage that you can feel the texture of the dough change, and through experience you know when a dough is right. Hand kneading also is good for gauging the hydration of the dough, as you can feel if it seems to dry or too moist and act accordingly. Through practice you get to know when a dough too sticky, and sprinkle just the right amount of flour on to get it just right, or add a few grams of water to open it up.

A machine is less work, but as you aren't feeling the dough as you go it's harder to gauge when it's kneaded right, and it's easy to overdo it and get a tough dough. With a machine it's also harder to know if the hydration level is right as you aren't feeling it. You can remedy that by stopping often to feel the dough, which is what some people do, and through experience get good results.