It's a workable technique, but the logic isn't wholly clear why it's
better than simply steering directly into the core.

Draw a set of concentric circles representing decreasing lift as you
move away from the core. Place your circle slightly off center. While
a widening of the turn puts you in a good position to move gracefully
into the core on the opposite side, it also steers you initially into
weaker lift and keeps you in it for several extra seconds (as your
rate of turn decreases with decreasing bank). Weaker lift, longer
exposure.

Also, as you shallow your bank, the glider opposite will begin to
catch up with you, turning inside, assuming he is not matching your
correction. And in fact, the shallower your turn, the more difficult
it will be to see since your wing blocks more of your view to the
rear, exactly where the other glider will approach you as you widen.

No danger. Simply requires an extra look before steepening into the
core.

If the gradient is strong, it's worth your while to move in quickly,
even if it briefly costs in terms of gliding efficiency. I may be
flying less effeciently, but I'm doing so in stronger lift, and I'll
return to optimum bank sooner, and centered on the core. The stronger
the gradient, the greater the payoff for letting one's impatience
rule.

As for safety, if I'm turning inside the other glider, I'm keeping it
in view. Shallowing your turn puts the other glider in your blind spot
and potentially in a position to keep your from moving gracefully into
the core. If I am breaking the established pattern, I'd much rather
keep others in view than to assume that they've seen me and depend on
them to adjust.

Steeper... gets you to better lift more quickly without traversing
weaker lift first. Shallower... well, I have to admit, it's more
graceful, though not necessarily safer, nor better for maximizing your
climb rate.