I have a domain that has been on the web for a long time.  It has hundreds of thousands of these links.  If you visit the pages where the links are placed they are rubbish directory-listings or mashup pages that contain paragraphs grabbed here and there from sites across the web.  The websites that host these pages are spam.

I have never disavowed any of them.  I don't worry a bit about them.  The only thing that I have done is add code to my htaccess file that strips parameters off of them.  Google has a service in Webmaster Tools that allows you to exclude parameters, but I'd rather handle it myself with htaccess than rely on Google to do it for me.

Google might consider it a "link scheme" - especially if the press release contains multiple links with keyword optimized anchor text.

You can read what Google has to say about link schemes here.

In my opinion it is bad to allow infringing content to appear on other websites.   These are duplicate content.  It is possible that they will outrank you in the SERPs or result in your page being filtered from the search results.   Also, if you work hard to produce this content then you want people coming to your site to see it - not to the websites of others.  If it appears on websites all over the web then why should people visit your website?   Finally, if these folks use the content and give you an attribution link, that communicates to everyone who sees it that your content is available for reuse.

Google says that they are good at recognizing the original source of content, however, I know from experience that they are far from perfect.  Some SEOs believe Google, and advise clients to distribute their content as a way of earning links.  I would not listen to them.

We tell infringers to take our content down and when they don't comply we either submit DMCA to Google, their revenue source and their hosting - or we have an attorney send them notice.    We are sending out three notices today.

I am going to say what I do and how I think that it works.  I am not saying that this is correct or best practice.

When I abandon a URL I do not place the redirect in the .htaccess file in the root directory.  Instead, I place an .htaccess file in the folder where the URL was saved.  That limits the size of my .htaccess file in the root directory.  I believe that reduces the amount of work that your server must do, it does not need to examine a very large .htaccess file.

If you use many folders to categorize your content then you will have small .htaccess files that are easier to manage.  From time to time you will be able to redirect entire folders instead of individual files when you abandon a product line or a category of content.

That's what I do.

Robots directives and rel=canonical can be assigned by .htaccess.  This is a very handy way to assign noindex or rel=canonical to .pdf documents, print formats, video transcripts, etc.  You can also use it to apply noindex or rel=canonical at scale.   Two  Moz articles (of several) that describe these are....

https://moz.com/blog/how-to-advanced-relcanonical-http-headers

https://moz.com/blog/htaccess-file-snippets-for-seos