I wrote an extension which does that; it keeps you on the Latest Tweets timeline and moves retweets to their own fake timeline, so by default you only see original tweets and quote tweets from people you follow:
https://github.com/insin/tweak-new-twitter#tweak-new-twitter
I've been using Twitter this way for years and consequently find the unmodified version completely unusable, so it was either learn how to do it on New Twitter or quit using it at all.