Are white units required to counterattack when the CR results is rolled, just as they are compelled to do so with a Counterblow? And I presume CA is a voluntary attack, and so white brittle units cannot take part?
All units must attack a Counterblow, White or Black. Counterattacks are a different concept.
So White units can sure counterattack, they just cannot voluntarily attack (meaning: initiate a combat with a Target marker) or take a step loss instead of retreating (21.13).
[14.7.3] Counterattacks: A CA result means that the Defender may treat the Battle outcome as “No Effect” and end it there or conduct a Counterattack.
If the Defender Counterattacks, remove any Support marker and discard played cards for that Battle and go back to Step 1 in the Battle procedure; i.e., start a new Battle repeating all of the Steps. This new Battle must include the exact same units as in the initial Battle, only this time, the Counterattacking player becomes the Attacker and no terrain CRT shift modifiers are used (although other Terrain Effects that negate armor shifts and multi- hex advance still apply, and non-terrain modifiers also)