I seem to be in the camp that counterspell doesn't hold a person, bind their hands, create a barrier, or silence them. Rather it nullifies the spell component itself.
A spell like booming blade requires a successful melee attack in order to work. As much as it is said to be apart of the spell description it is not the spell effect. In this specific instance
You brandish the weapon used in the spell’s casting and make a melee attack with it against one creature within 5 feet of you. On a hit, the target suffers the weapon attack’s normal effects
and then
becomes sheathed in booming energy until the start of your next turn. If the target willingly moves 5 feet or more before then, the target takes 1d8 thunder damage, and the spell ends.
Both as the SymantecSomatic and Material component, the caster is free to move. Counterspell doesn't prevent such an action. Even the verbal component the words may still come out, the caster isn't magically silenced, we have a spell specifically for that.
It would literally be as though the spell fizzles out, but none the actions leading up to it fizzling out.
