I'm asking more for a policy perspective. I called the brokerage firms I use and asked about volunteering myself for assignment if a written OTM option becomes ITM and a holder somewhere exercises.
In a different question the accepted answer mentioned that the exchanges assign randomly for fairness. I don't see why allowing volunteers wouldn't be fair. Allowing volunteers would decrease the risk for those who don't want an assignment and increase the chance for those who do.
I picture something like: when an exercise order is received, assign randomly among volunteers and if the volunteers run out switch to the pool of non-volunteers. The exchange could assign with uniform randomness to a broker and if the broker has no volunteers pick another broker. Alternatively brokers could report their number of volunteers and then the exchange could assign with a probability weighted by that number.