A cordelette used to set up a 3 point anchor will have three loops of rope above the knot (one per piece) and three loops below. The knot itself will have 6 strands of rope running through it. (This eats up almost 2 meters of cordelette length alone.)
If you cut a single strand the location of the cut hardly matters; you will still have two independent loops both above and below the knot.
(If your concern is that the entire loop of cordelette is no longer a closed loop, then why would you consider a cordelette to be a closed loop at all? After all, whichever knot you used to tie it into a loop could similarly "unravel". Fortunately we are not using frictionless materials, and so knots actually hold.)
While redundancy is often talked about, in actual use it's mostly applicable in cases where the security of a piece of equipment is uncertain. Thus it is common to double up on bolts or triple up on cams, whereas a good-sized tree or refrigerator sized block of stone can be considered sufficient. Similarly, top-rope anchors are usually unmonitored, so you use extra carabiners at the powerpoint to ensure the rope doesn't unclip itself.
In multipitch anchors where someone is at the anchor to keep an eye on things, using a single sling to connect a pair of bolts and a single locking carabiner as the powerpoint is relatively common.
Your belay device is attached to a single belay loop, your climbing rope (at least in the US) is often single, your personal anchor (or sling, or bit of rope) is similarly single, and I would argue that your harness tie-in points are better described as "complementary" than redundant.
What makes the absolute strength ratings of equipment less important is the rope itself; its elasticity lessens the force on the rest of the equipment. A fall hard enough to break a sling or cordelette is going to do very bad things to your spine and internal organs. (Even a factor two fall on climbing rope should not have enough force to do this.) Thus, if a cord breaks in actual climbing, it's probably because a large rock fell on it or it was cut by a sharp edge.