It goes back to the days of wide lands and narrow grooves. Hard lead is very difficult to load in this rifling form.
Green Mountain barrels with their narrow lands will allow harder lead to be started much easier.
I have a 16 bore barrel with narrow lands that shoots lead or WW interchangably. Its a .672-.6725" bore with 8 wide grooves .008" deep and will load a .662 WW ball easily with a .012 linen patch and it shoots as well as lead with a .662 and .022 cotton ticking patch or a .672 lead with a .012" linen. The 672 from hard WW with linen patch will not start without extreme effort no "crush". Did not fully start this combo.
This barrel is not very accurate with any combination though and is going back to its maker for a inspection. But historically hard lead works well if the rifling form is suitable.
Wide lands and narrow grooves will not work well with hard balls. To much tough bullet metal to squish. A hard ball will enhance penetration on tougher animals. Not really needed for deer size or most black bear if the ball size is adequate.
Historically using soft lead on large/tough animals is a mistake, especially African/Indian heavies.
Some years ago Turner Kirkland (Founder of Dixie Gunworks) tried to shoot an African Elephant with a 4 bore using soft lead balls. Penetration was only about 24" with massive expansion. Had he done his homework he would have known the old time heavy game hunters hardened the balls. Had he done this it is doubtful the PH would have had to finish the animal which Turner shot twice.
With hardened balls a 10 bore will suffice for lung shots on African Elephant. See John Taylor's "Pondoro". A 4 or 5 bore with hard balls will even stop charges according to Samuel Baker.
For animals like deer a 50-54 lead RB will give all the penetration needed. For elk sized animals I would rather have a .62 caliber though a 54 will work Ok for lung shots with soft balls. For dangerous North American stuff like Gbear the 16 bore is probably minimum regardless of alloy though I would shoot hardened lead at big bears because you really need sure penetration.

Dan