What do you mean “there’s no choice”? Should we get rid of butter knives because we have combat knives? I don’t understand where you’re coming from. Why not have some styles that are strictly better than others? If you started with two styles and one was better in every way, sure that’d be pretty weird, but you’d generally have to learn boxing, see below.
The current status of styles and skills as I understand it (and from memory, so details may be off):
The given attack has melee, unarmed, bashing, cutting, and stabbing components. (some of these are exclusive, stabbing and cutting definitely are, I think unarmed with no weapon is bashing-only, you CAN trigger “unarmed” with a weapon if it has the “unarmed” flag, like brass knuckles).
For a given attack, the skill used is melee + the highest applicable specialized skill.
All a selected style does is apply various situational bonuses, and throw additional techniques into the pile to be activated.
This is orthogonal to the brawling versus boxing thing though, my point there is boxing would have better situational bonuses and higher quality techniques available to it than brawling, because boxing is based on medical and kinesthetic studies of the human body as opposed to trial-and-error.
As for formal versus ???.
I was operating under the assumption that acquiring the boxing (or any other non-default) style would involve either acquiring training from an NPC, a pre-cataclysm trait, or a training manual. I think that’s what you mean by “formal training”, but I’m not sure.
The alternative is “informal” styles like “brawling” and “wrestling”(somehow differentiated from other formal wrestling style, I have no idea what they are) and possibly others (street fighting?), that you’d just pick up as you progress in combat ability. It’s better than nothing, but just wouldn’t be as good as the styles that have been honed by years and years of practice by experts.