I use feedly because it's where I landed after GReader; I don't love it, but it has worked continually without bothering me enough to think about it.
But one day I want to look into alternatives, and the number one thing in my wishlist is to be able to scrap sites that crop the full article in the feed. Going from the RSS client to the browser to the reader mode in the browser is such an absurd friction.
Edit: Well, after 12 years, that day ended up being today. I found a client called FeedMe that syncs with Feedly and can load the full article inside the client. It also has some other features that I was looking for, like filters. There might be more clients like that, but this is the first I found. I shouldn't have been so lazy all this time.
I use BazQux (https://bazqux.com/) as it was the closest to the old Google Reader I could find.
The developer also set up their own instance of FiveFilters Full Text Rss (https://www.fivefilters.org/full-text-rss/) for use with that reader to do fetch the content. I typically use this as proxy for any feeds I'm going to add where the author didn't provide the full text.
Other than that: * The BazQux web interface has a button to fetch the full text content of the article. * As you noted, FeedMe on Android can also switch to web mode to fetch full content.
I prefer the Five Filters way because then I can go through my feeds offline while in transit