There's nothing about the NT kernel that needs to be rewritten to implement a POSIX or SUS compliant user-mode subsystem. They once had a Windows Services for UNIX (SFU) subsystem that was POSIX compliant. The new "Bash on Windows", officially called "Windows Subsystem for Linux", appears to be targeting the Linux Standard Base (LSB) and not striving for POSIX or SUS compliance.

LSB is mostly a superset of POSIX. POSIX is a subset of SUS. OSX is SUS compliant, though not POSIX certified. Windows is POSIX certified though not SUS compliant. And no one is LSB certified except a few Linux Distros.

This leaves me wondering exactly what target Microsoft should be aiming for since everyone seems to be playing by their own rules. It's like playing Monopoly with your friend's family who has their own house rules that aren't really like your family's house rules both of which are incompatible with the official rules.