As an exercise I once went through the process of manually requesting my information removed from most of the top brokers.

It would be difficult to automate because the opt-out processes usually aren't straightforward like unsubscribing from an email list. Many sites make it purposely difficult and involve going through multiple steps, providing verification like a drivers license, and email confirmations.

Here is a really good check list of different brokers: https://inteltechniques.com/data/workbook.pdf