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You're absolutely right, Mark. That's why I carefully crafted my last
post with a weasel word or so, saying it's 'one way to indicate...',
and that it's 'visually obvious everyone starts' the same. Of course,
once you move, the symmetry is usually broken. Chieftain Chess can be an
exception - that game is capable of being played entirely symmetrically,
with opponents casting patterns at each other the entire game - but in
most variants, this is not possible. So I've looked for other methods to
ensure fairness. Two of them are larger boards and short-ranged pieces.
FIDE chess is played on a rather small board with a comparitively large
number of unlimited-range pieces. I do think those 2 facts are what give
white so much of a first move advantage.
I've also been looking at moving away from strict bilateral symmetry in
my most recent games.  [But nobody's  been looking at them, so it's a
wash! ;-) ] Anyway, most enhancements to black, who moves second,
unbalance the game the other way, proving unsatisfactory.