If you're going to run the OS, you have to make sure it compiles and runs the bootloader and its installer. The toolchain could be different enough for that to fail. And you do boot into a reasonably small OS and continue from there. That's what BLFS is all about.

TBH, though, the only lesson you learn from BLFS is that value of package managers.

If you like the idea of everything being purpose built for your computer, then after you do LFS you should switch to gentoo.