“The crystal is the heart of the blade. The heart is the crystal of the Jedi. The Jedi is the crystal of the Force. The Force is the blade of the heart. All are intertwined. The crystal. The blade. The Jedi. You are one.”
Crystals often have a mystical quality to them, even in real life (not that I subscribe to it personally). In Star Wars, I think it fits just fine for the Jedi to view crystals as a spiritual asset that resides in their weapon of self-defense. Think about it; the crystal is merely an additional instrument in the weapon for the Jedi to further “see” the ripples of the Force around them. It vibrates and resonates within its surroundings, and to a non-Force sensitive, sure they could pick up the weapon and ignite it, but they would not sense the extension of the Force. Yes, Jedi can already feel disturbances in the Force, but perhaps the crystal inside a lightsaber is more like a precise and amplifying instrument when engaged in intense combat. Useful to “see” how and when an opponent will strike, similar to how the hairs on our bodies can detect micro-movements.
To sum up, no, not every Jedi needs a lightsaber. But it’s nonetheless a sacred weapon and useful so long as the wielder is well versed with the Force before hand.