most people don't realize it but the jacketed fmj's for calibers like the 45acp & 9mm are a form of hb bullet. All's 1 has to do is turn a fmj upside down and look at the rebated lead core and the extended lip of the metal jacket at the base of the bullet
Lots of different reasons for a hb bullet. Keith used a hb bullet design to take the weight out of his swc designs to be able to have faster/flatter shooting loads. As others have already stated for accuracy. Consistency comes to mind when I think of hb bullets. Again as others have already stated a hb bullet will work/perform equally well in a tight bbl or an oversized bbl.
Higher velocities along with consistent velocities over a wide range of firearms is another reason for a hb bullet. The fbi ww 38spl load used a hb bullet. Consistent performance shot after shot in a wide range of firearms.
A special order cramer mold that casts a hb swc for the 45acp. This mold was specifically designed for the surplus 1917 45acp pistols. The 1917 pistols were bullet with parts that had hude differences in the diameter of the cylinder throats and bbl.'s. The fmj jacket's skirt that hung down helped with these differences but there was still huge differences in velocities from firearm to firearm with the same lots of ammo.
It wasn't uncommon to have a 1917 revolver with an oversized .457" bbl on it. That bullet mold pictured above could cast a .454" bullet with soft lead. It's hard to get any larger of a bullet in a 45acp case without swaging the bullet down or getting the oversized reloads to fit in the cylinders. These cast hb bullets can be sized to .452", loaded in 45acp cases and be fired in the .457" bbl.'s of the 1917 revolvers and they would expand/seal them with no leading.
A 44spl version of the fbi's 38spl bullet. It's a 210gr hp hb swc
1000+fps from a snubnosed 44spl with a 18,000+psi load. Not only does the hp nose expand, the hb expands.
hp expansion ='s .625"
hb expansion ='s .500"
bullet length ='s .75"
compressed bullet length ='s .500" .
9mm's tend to do better with smaller/narrower hb's. The small case capacity, tapered web and high pressures of the 9mm are hard on traditional hb designs. I made 3 or 4 hb pins testing different designs in a lyman 35870 hb mold. the 35870 was 1st sold in 1900 and was designed for the 38lc. I ended up with a narrow hb pin that extended up to the top of the 2nd drive band and left thick hb walls at the base of the bullet.
Some people like hb bullets, others not so much. Some think they work, others say no. Myself I've had over 30+ different hb molds over the decades for the 9mm/38spl/357/44spl/44mag/45acp. Along with swaging different hb bullets for those same calibers. All's I can say is without a doubt they flat out work enhancing performance and accuracy.