When sizing a subpanel feeder for a one- or two-family dwelling under NEC rules, after all the load calculations are done, there's another question that must be answered. It is this: does that subpanel serve the entire load associated with the dwelling? In other words, are there (or could there be) circuits added in the main panel so that some of the load is served at the main panel and other of the load is served at this subpanel?
When the entire load associated with the dwelling is carried through a given feeder (or a service), NEC allows a little break in the wire sizing. The wire may be sized for 83% of the overcurrent protection limit. For example, if the overcurrent protection is at 200 A the wire may be sized for 166 A.
Feeders and services often use THWN or XHHW insulated wire and are sized for 75° C. When using aluminum conductors the 4/0 gauge with 180 A ampacity fits the bill for 166 A sizing. When the 83% de-rate does not apply, though, aluminum 250 kcmil would have to be used to meet the full 200 A ampacity.
A short feeder, or one where conduit size is expensive, might opt for copper conductors instead of aluminum. The same de-rate rules apply.
This does seem counter-intuitive. I don't know but I could speculate that the NEC load calculation procedure causes a whole-home load to be a little over-stated, so they give a little back in the service/feeder sizing. Such excess may not be incorporated in the general case, though, so no de-rate is offered generally.