Both the Rosh and the student should present their case and the boy should then leave.
Completely unrealistic. No menahel would or should be involved in a public debate with a student.
What you are suggesting would also be terribly humiliating for the student, as you point out later in your post, so you haven’t helped matters, you’ve just replaced one humiliation with another.
Your entire opinion is predicated on your considering what this (fictitious, IMO) student did as “no big deal”. Most yeshivas do consider such socializing to be a big deal, and the students know it (which is why just explaining to him what’s wrong is not sufficient).
I’m not suggesting that a boy be thrown out for this; it’s much more complicated than that, and yes, it’s devastating for him., but a fair discussion has to consider the seriousness of the issue. The fact that the socializing took place in plain sight also indicates that the boy is not even embarrassed, which takes things to a different level.
I’m not sure why, Aries, you are fixated om the “moser”. If the menahel confirmed things independently, he must deal with the issue even if he became aware of it through an individual who may have had the wrong motivation.