De-indexing means a page stops appearing in search results. It does not mean the page is deleted. The page keeps sitting at its own address, and anyone who has the direct link can still open it. What changes is that people who go looking, by typing your name into Google, stop running into it.
Why that distinction matters
Almost nobody finds a damaging page by typing its URL from memory. They find it because it ranks when someone searches for you. Take it out of the index and the discovery path disappears, even though the file on the server has not moved.
What it does not fix
If someone already has the link, they still have the link. If the content is mirrored across a dozen aggregator sites, each of those is a separate URL that has to be dealt with on its own. And a page that is out of Google is not automatically out of Bing, which is why we handle them together.
How to think about it
Ask yourself how the people who matter would actually encounter the page. If the honest answer is a search, then de-indexing solves your problem. If the honest answer is that your industry already circulates the direct link, it will not.