The Israelites' direct experience with Divine providence was meant to show them that their military victories did not come from their own strength. As they overcame the nations they had already defeated [מצודת דוד], it became clear that these triumphs were the result of God actively fighting for them [מצודת ציון]. Witnessing these great signs and wonders proved to the nation that God's eternal hand accompanied and saved them at every step [מלבי״ם, שטיינזלץ].
The physical act of seeing these events unfold raises a deeper concept regarding the nature of miracles. Generally, if a person experiences a miracle that does not occur due to their own personal merit, they are not allowed to actually see it happen. Because the Israelites physically witnessed these wonders, they might have incorrectly assumed that their own abundant merits earned them such open intervention. To prevent this misunderstanding, it is emphasized that God fought for them through His attribute of mercy. When a miracle is born from Divine mercy, a person is permitted to witness it even if they lack sufficient personal standing. This is exactly why the Israelites were able to watch the downfall of their enemies with their own eyes [חומת אנך].