Rarity is relative. Considering how much OP cared about that sword, I assumed it wasn’t something he was looting every other day.
Are you asking why people would rather run risky dungeons on a throwaway char than one they actually care about? Because both have the same chances at loot but one is more expendable than the other.
Once you’ve looted a good item you really want, however, whatever character you got it on immediately becomes much more valuable.
That’s when you should ask yourself: “is the loot I could get from this next dungeon worth risking the loot I already have or not?”.