That's a great idea. I would definitely use a service like that.
Source code of a slightly older version available at: https://bitbucket.org/fivefilters/full-text-rss/src/master/
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.
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.