If you want to have a Zig compiler written in Zig, you need to bootstrap it once initially. Cross compilation makes it so you don't need to do that again when you want the compiler to work on a different architecture. Of course, there's the question of why you want to self-host your compiler (instead of keeping the C++ one): - dogfooding identifies problems & helps prioritizing - it demonstrates that the language is suitable for serious projects - most importantly, Zig developers prefer writing Zig over having to use C++