I am a US citizen. For many years I tried exercising this right while remaining silent.
I’ve been kicked out of a border control point in northern Vermont in February in a snowstorm after a four hour interrogation. (They sent the bus without me.)
I’ve been arrested and locked in a room for twelve hours with no food or water or medication.
I’ve been endlessly harassed and interrogated on other entries even when not exercising 5th amendment rights to silence.
In all cases they eventually let me go without charges.
They have to let you enter, but they don’t have to do it quickly or humanely.