If you have hum in your system it probably is a ground issue. You should consult a licensed electrician. Multiple ground points can create voltage differential... bad. There are options if you are having noise problems, which often show up in older installations where multiple neutrals are tied together for expediency. Electricians are familiar with grounding problems, they can play havoc with computers. Maybe not so familiar with audiophile equipment, but many of the same issues. The ground stud is there for your convenience, Some of the older 2 wire components ground through the shield of the interconnect. When that is not sufficient, or an incomplete circuit, the ground stud, or a cover screw, can be of use. Most equipment in the phono side benefits from a physical ground, BTW, if you have hum from an older 2 wire turntable, turn the plug 180 in the outlet, realigning the neutral. Be careful, you can do worse than hurt yourself (or someone else). Consult a pro, and don't mess with the panel.
Earth (isolated) ground vs. wall outlet ground.
Looking on my 200amp main panel I notice that the neutral (white) wire bus and the ground (bare copper) bus have continuity. Wouldn’t it be better if my interconnected rig had it’s own earth ground thereby isolating it from feedback from the neutral wires? If not (NEC rules, Ott’s Grounding Myths, etc.) why is there a ground lug on some of my pieces? Surely it’s not there for decoration. I can’t imagine a manufacturer adding a useless item (adding cost) in a hidden place if it didn’t have specific function. All my pieces are connected by balanced XLRs (except the speakers) and the balanced XLR has unified grounds. Inquiring (and in my case sometimes simple) minds what to know.....