Posted this in another reply, it's a project I've worked on for a while, works essentially the way djhworld describes: https://fivefilters.org/content-only/

Source code of a slightly older version available at: https://bitbucket.org/fivefilters/full-text-rss/src/master/

I think other people in this thread are running services that do a similar thing.

My crisis of conscience was around storing the full text of the articles on my own server and then presenting them as a new feed on my domain, e.g. https://mydomain.com/feeds/eurogamer.xml

Everything in the feed is that gets generated is exactly the same as the original feed (canonical link to the actual article, publsh date, author etc) the only difference was the text in the body of each entry.

It's likely that unless you can claim status as a library or some other exception to copyright protections, as a commercial entity providing that service without compensating publishers, such a straightforward violation would get a bunch of takedown requests and eventual lawsuits for failure to respond to those requests, along with more suits if publishers have no easy way of opting out.

As a personal tool you built for yourself and your friend(s) nerdy enough to understand it, I wouldn’t worry too much about it, as long as no search engines index your site and no one finds out about it.

And others would definitely sue a service like that. (I'd use it, too, but I understand why it won't happen.)