Is there any story justification for "traversing the white light"?

Solution 1:

No, there is no known story justification.

However I have some speculation:

I can't find the source for this, but IIRC the in story explanation for invasions, summoning, and miracle resonance is players interacting with time in 'interesting ways'.

If the above is accurate, then I speculate, one reason for the the fog barriers is a boundary across time/space where these interactions with time are occurring. In multiplayer non-boss fog gates reappear and forces you to interact with the invader or the boss.

Solution 2:

I've found a website that states that the fog gates are a result of the mass fog that has engulfed the land its an adaption of the demons souls story. As a result of the fog it was hard for the undead to travel the world, they had to travel through the fog to progress. that's the only story justification for traversing the white light.

Here is the small wiki I used: http://darksouls.wikidot.com/fog-gate