I'd prefer the current behavior to remain. The benefit to botmakers of the ability to control the notifications that their bots generate is, I think, a relatively small use-case when compared with the vast majority of notifications that your average Twitter user receives (I can't think of many other benign use cases). As harassment is a (unfortunately) continuing problem on Twitter, being able to stay on top of your notifications is important for the personal safety of a lot of folks.
If, for example, a high-follower user were able to conveniently, and without generating a notification, direct their followers to a specific person's account with the intent to harass in the middle of the night or some such, this change would allow that behavior. (With the proposed change, it would in fact be of little difficultly to create an entire Twitter client dedicated to discussing folks surreptitiously.)
Even without malice, a retweet or mention from a high-follower account can generate a lot of unwanted attention - it's often helpful to have some kind of warning of that and be able to take your account private before more people jump in and dissect the rest of your timeline.
As you note, @stefan, re: the person being discussed:
it's trivial to remove the @ from someone's username, and that would be okay.
Yes, it's trivial to do so, but I'd argue that that trivial barrier dissuades a raft of (often ill-meaning) Twitter users who cannot be bothered to search for a user's profile or the tweet in question. In fact, you acknowledge this, stating:
including the person's username without an @ creates a sub-par experience for those who'd like to either respond or see more tweets from the same person.
This is especially true if an old tweet (usually taken out of context) is dredged up to, let's say, ruin someone's day. The majority of users aren't going to bother dealing with a hundred "pages" of infinite scroll just to quote tweet that with something offensive.
Just my thoughts on the matter. If this were 2009 Twitter, I'd probably be with you on this, but it's unfortunately not.