The summary you gave is excellent. The various brokers have assorted policies from not participating, participating ONLY if you have an account with X dollars and call, to others that enroll everything.
When I complained to a prior broker they said too bad. I moved everything including my family pension trust to TD Ameritrade. Opened 4 seperate accounts, was paid $2400 to move my money there and other than the usual glitches have good service.
Do have one ususual happening, one of my discount companies - TD calls them "Specials" and does require a notification and seperate sign up - dropped about 7% between the dividend pay date and the date they got paid from the transfer agent in Canada. Instead of accepting the shares at the discount, they bought in the open market as it was cheaper for their customers.