Yeah, I think that was the idea behind the suggestion for choosing handedness or movement style; they'd show no matter what.
My own preference for that kind of design was simple: You don't have a helmet (or any form of headgear). Period. No obstructing headgear, no problem.
But the truth is that, no matter what, games don't have the finesse to let people recognize other people by facial features alone. We (as humans) are extremely good at recognizing people and primarily through their faces, then gait (see above), then general body shape and facial hair (yep, we're more sensitive to face shape than hair), but beyond 10m, a game screen doesn't provide enough facial details to let us work our brain facial magic. Why do you think we still have floating names over people's heads?
So the most important customization feature should be... equipment and tint. The real reason things like Cosmetic Slots and Slot tints and the like are popular is that they let you pick a specific look, and what's more important, keep that look across equipment upgrades. Because if you have to offer the player a dilemma between upgrading stats and looking like him/herself, you've lost.
So, rather than having people start as half-naked people in drab rags, let them pick from a selection of outfits and appropriate tint sets. If you want to develop an in-game visual identity, your identity should begin on day 1, not change every other day until you get that "special look" three months later. Because, as interesting as it is to have to "collect" the look, you are also training them during that time to ignore the visual clues to people recognition, since people will change appearance where it matters every week or even days. Funnily enough, this is a big deal on super-hero themed MMOs. Your look defines who you are. But there's no reason your look shouldn't define who you are in game.
The people who complain about the lack of showing up their e-peen have to realize that, of course, this precious equipment is their identity, but, by allowing people to have rare identities, you deny having an identity to everyone else. If your top gear makes you a celebrity, then you do lump everyone else into the same scrub identity. It's a common aspiration, though.
