Darren,

Your comments about "strict permissions requirements" of .ssh helped me investigate my password-less ssh login issues with the Windows Subsystem for Linux (WSL). Also, your comments about the permissions and which side controlling the file permissions was helpful. But my solution was a bit different and, in particular, the use of the ln command was different.

My approach was to allow the WSL to control the file permissions of /home/comperem/.ssh and everything in there (known_hosts, id_rsa, and id_rsa.pub)

Previously I had changed the WSL bash HOME environment variable to /mnt/c/Users/comperem by editing the WSL system-wide bash.bashrc file in /etc/bash.bashrc with this:
export HOME=/mnt/c/Users/comperem

Then, in WSL's bash, after running 'ssh-keygen -t rsa' and hitting return to all defaults with no passphrase, the WSL files appeared in their expected location with proper permissions:
ls -l /home/comperem/.ssh/
total 4
-rw------- 1 comperem comperem 1679 Jul 21 11:46 id_rsa
-rw-r--r-- 1 comperem comperem 397 Jul 21 11:46 id_rsa.pub
-rw-r--r-- 1 comperem comperem 444 Jul 21 11:46 known_hosts

Notice the permissions properly implemented with WSL's bash: -rw-r--r--

This is where my solution differs. The ln command is similar to the cp and mv commands:
ln -s src dest (or ln -s TARGET LINK_NAME which is the same conceptually)

Creating a symbolic link to .ssh in the Windows home folder to the WSL .ssh with:
ln -s /home/comperem/.ssh /mnt/c/Users/comperem/.ssh

results in the proper permissions for the entire contents of the .ssh folder on the WSL side:
comperem@matrix:~/.ssh$ pwd
/mnt/c/Users/comperem/.ssh
comperem@matrix:~/.ssh$ ls -l
total 4
-rw------- 1 comperem comperem 1679 Jul 21 11:46 id_rsa
-rw-r--r-- 1 comperem comperem 397 Jul 21 11:46 id_rsa.pub
-rw-r--r-- 1 comperem comperem 444 Jul 21 11:46 known_hosts
comperem@matrix:~/.ssh$

Then remote login with ssh is passwordless via the public keys as expected.

My solution is a bit different but your post helped.