I have always thought of basic sizing this way:
The cable must be sized to carry the load and as such the load will determines the cable size. The cable size selected must consider any derating factors which may apply.
The the breaker is then sized to protect the cable. Often times there are those who are intent on getting the cart before the horse.
Isn't it true that the cable is sized at 125% of the continuous load + 100% of the noncontinuous load? If the computed load is based upon 210A then the cable size selected must be sized to carry that load. If so a 4/0 cable rated 230a is selected based upon the standard rated cables that are available.
If the cable is rated 230a then you are allowed to use a breaker with the closest rating above 230A which is a 250AT. If I recall correctly you can do this with breakers up to less than 800A where you are then required to use the the next standard rated breaker below the cable's rated amperes 800A and above.
This is what the NEC art 240 says about it which I don't think has changed for years now:
Devices Rated 800 Amperes or Less. The next higher the conductors being protected) shall be permitted to be used, provided all of the following conditions are met:
(1) The conductors being protected are not part of a multioutlet branch circuit supplying receptacles for cordand-plug-connected portable loads.
(2) The ampacity of the conductors does not correspond with the standard ampere rating of a fuse or a circuit breaker without overload trip adjustments above its rating
(but that shall be permitted to have other trip or rating adjustments).
(3) The next higher standard rating selected does not exceed 800 amperes.
The next higher standard rating selected does not exceed 800 amperes where the overcurrent device is rated over 800 amperes, the ampacity of the conductors it protects shall be equal to or greater than the rating of the overcurrent device.
As far as breaker being 125% rated or a breaker applied at 80% of its rating? If the cable is sized a 125% of the continuous load then sizing the breaker based upon the cable ampacity which automatically applies the breaker at 125%. Or the reciprocal is a breaker which is automatically applied at 80% of it's rating. How cool is that?
Simple, size the cable to carry the load, size the breaker to protect the cable.
I know that there are exceptions based upon specific conductor application.