RSS was awesome in late 2000s during the Web 2.0 mania and it was common to see entire site's contents reproduced in their feed. By 2013 I'd argue many sites had realized giving their full text content away with no ads in the RSS feed wasn't exactly helping their bottom lines and started delivering ads and content snippets instead. The intent of course was to drive you back to the site where ads can be served more reliably. When these practices became widespread RSS quickly lost its shine for me and others I'm sure.
All of the RSS readers I used at the time other than the Reader web app also had the option of fetching full text or loading the feed in a browser frame to avoid the fragment problem. Some of that was simply performance: a busy site publishing full text could generate some massive XML files which take time to transfer and parse.
Also, why is it a problem to show ads in feeds? Annoying ones, sure, but I'd be happy to have ads (or pay for a subscription) if that meant that places could pay journalists.
Google Reader was the first RSS client to incorporate social features with RSS. To that it added an extremely fast web client (I can't think of any web client that even existed before), and syncing across devices.
A LOT of software in the RSS ecosystem relied on Google Reader for their syncing capabilities. It had basically become the defacto backend for the majority of RSS readers. As an example, I used NetNewsWire for my RSS reading, and while I rarely (never?) used the Google Reader interface, NNN relied on my Google Reader account to backup and sync my feeds.
Google Reader had basically become essential infrastructure in the RSS ecosystem.