Does Kylo seek Luke's original lightsaber because it is Vader memorabilia, or is it a legitimate dark side relic/symbol of power?
After all, the lightsaber Luke wielded was also Anakin's lightsaber, and thus the same blade that slew countless Jedi and Younglings during Order 66, and subsequently the remnants of the Separatist leadership. Figuratively, it was a weapon of great darkness.