In 2006, Cheeger and Kleiner proved that the Heisenberg group fails to bi-Lipschitzly embed into $L^1$. The authors remarked that their proof should hold for every Carnot group $G$ that satisfies: for every finite perimeter subset $E\subset G$ and $\operatorname{Per}_E$-almost every , every tangent of $E$ at $x$ is a half-space. While such property remains elusive, Ambrosio, Kleiner, and Le Donne made significant progress by proving that every Carnot group satisfies: every finite perimeter subset has the property that for $\operatorname{Per_E}$-almost every $x\in G$ , there is some blowup of $E$ at $x$ that is a half-space. We use the result of Ambrosio, Kleiner, and Le Donne, together with the framework of Cheeger and Kleiner to show that nonabelian Carnot groups fail to bilischitz embed into $L^1$. This is joint work with Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne, and Sebastiano Nicolussi-Golo.