A thrust stage puts the actors in the midst of the audience. The proscenium arch through which one looks into a recessed stage distances the actors from the audience. It as if we were looking through an invisible fourth wall of a room. If characters exit through side doors you know you are dealing with a proscenium arch. With such a stage arrangement it is more natural to preserve the illusion that stage events are actually occurring, with the audience in the role of voyeur, unsuspected by the actors.
Thrust stages are older.
The first plays in the Western tradition were given in Greece in about the sixth century BCE in the open air. The audience sat on a semicircular hillside and the chorus and players performed in the open air of a flat space at the foot of the hill. Later, three doors were added were added to the skena so that the actors could enter or exit through them as well as through the passages on either side of the acting area to the right and left of the skena . They could also play scenes on top of the skena . Shakespeare's stage in the latter sixteenth century derived from this Classical tradition and from other influences such as the great hall of a Tudor mansion where plays were often performed, and the Medieval tradition of playing on moveable wagons called pageants .