Unlike Lucas’ prequel Sith, it makes sense for Kylo Ren to carry a lightsaber because he was once a Jedi (the Emperor specifically called the light saber a “JEDI weapon” not a Sith weapon).
I usually try not to defend the prequels, but… the prequels depict four Sith: Maul, Dooku, Vader, and Palpatine, half of whom were once Jedi (Dooku and Vader).