Is there a simple explanation why RISC-V software has to be built on a RISC-V system? Why is it so hard for compilers to compile for a different architecture? The general structure of the target architecture lives inside the compiler code and isn’t generated by introspecting the current system, right?

Under specified build dependencies that use libraries/config on your host OS rather than the target system

You can solve this on a per language basis, but the C/C++ ecosystem is messy. So people use VMs or real hardware of the target arch to not have to think about it

Cross building of possible, but it's rather useful to be able to test the software you just built... And often enough, tests take more resources than the build.