The remise is important in sabre because of two elements: first, that an attack is over when the front foot lands in the lunge.
(In theory, all attacks end in a lunge or flèche, and the fleche is forbidden in sabre.)
Therefore, if the attacker's front foot lands before their blade hits their opponent, their action is automatically a remise.
Also, because any contact between a blade and the opponent's target area will set off the scoring apparatus, many fencers whose attack has failed will keep their arm extended or make a quick second cut to attempt to catch their opponent's arm during their riposte.
Thus, a pair of foil fencers may, upon finding their thrust have not landed, remain in a lunge position and repeatedly remise hoping to be the first one to score a touch.