I suspect the user content is the root of the problem. 500 hours of video is being uploaded every minute. YouTube has to transcode and store everything, and be ready to stream it at a moment's notice, even though the vast majority of videos probably get only a handful of views (if any). That's a lot of unused resources that have to be paid for by subscribers and advertisers.
If they were to charge just a little for uploads then content creators would be more inclined to consider whether their upload is of interest to anyone else, and that might take away a lot of the waste.
I'm 98% sure you can still log in again, it just invalidates the access token that Reddit has received from Google. The effect is that when you log in next time you end up at Google's authorization screen where you have to explicitly give Reddit access again.