For a long time i thought the idea that my reply, not a quote, just a reply, to a tweet gets posted to my main timeline / follower's timelines...is also a bad idea, but I guess this also was designed for 'engagement' too
Your followers will only see your replies if they also follow the account to which you're replying or if someone they follow retweets the parent or your reply. Otherwise, users will have to visit your profile and slide over to the Tweets & Replies tab.