Yes yes that’s exactly it. You see nipples are sensitive and boobs tend to jiggle and sway around when one moves, it can get very uncomfortable. So a bra reduces friction and accidental brushing against objects and clothing, helps support the weight and yes also helps shape the bosom. All that.
The original purpose of the bra was to let women move freely without fearing their breasts might pop out of their dresses iirc. But I think women used to wrap their chests with a tight cloth if they had to heavy physical work before bras as we know them today. Take this with a grain of salt, I didn’t fact check any.