Well, I can't really tell you how long their roots last, but I can give you some guidance on other things you mentioned.
What you are seeing in the root (coloration wise and shriveled) is based on age and/or growing conditions. Roots that are white have something called veluman (spelling?) on it which basically helps protect it. When you water it you will see them turn green. The bright green is more of a fresh root that still has yet to fully develop this protective skin. Please don't quote me on that information because it may be off a bit - learning this stuff as well.
However, the recommendation for repotting and cutting the roots is more to the fact of the potting medium breaking down and checking the roots to ensure it is still healthy. It never hurts to clean up your roots because otherwise the dead one's or dying one's will just add to the decomposition of your potting material. Since the roots need to "breathe" they cannot be in decomposing material as it will sink and suffocate them. Likewise, the decomposing material may increase the chances of infections, unwanted insects and nutrients you do not want it exposed to in such high quantities. Not to mention that decompossing medium retains much more water which would drown the roots.
While I can't say when the roots die off seasonally, I can tell you it does happen. Generally, phal's are pretty good at sending out new roots at all times of the year.
It is very important to clean up the roots (prune the dead or dying ones off) as was previously explained it could lead to infections and other issues if left in the pot to rot.
Not being a biologist, I can't really tell you what they do in nature - but your last comment about them falling off naturally would seem to make sense based on my limited knowledge.
Hopefully someone far more enlightened than I can chime in on this too. I'd love to learn more as well.
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