I fully share your sentiment. Tip, though: threadreaderapp.com will proxy them for you if you do really want to see them for some reason. I've also heard nitter.net mentioned, but haven't tried it yet.
I mostly use theoldreader.com, which doesn't, and honestly don't mind they don't capitulate and work-around privacy walls. Watching twits tweet with twats is mostly a non-starter anyways, nor would I believe anything I see there any more than facebook or other scandal rag links anyways.