I'm trying to have an unattended remote PC log some data on my home PC.
According to man sshd, I should be able to put a command in authorized_keys.
The key I'm using is a special key that isn't used elsewhere.

In my ~/.ssh/authorized_keys file on my desktop:
Then to write the data, I issue this command on the remote machine, where desk_pc is the IP of my desk PC:
This doesn't work.
I think my desktop it's trying execute the received text instead of cat it to the log file. This is displayed on the remote machine:
Do I need a pty? How can I get stdin written to a file without a pty if I need one?

How do I get it to execute the /bin/cat command, not the received text?

Try copying your id idenity.pub file to the remote server. This should allow you to ssh without a password.

If it does not work after that you may also need to check permissions.

For passwordless authentication to work four criteria need
to be matched:
a) ~/.ssh *must* be 0700.
b) ~ must *not* be world or group writable.
c) ~/.ssh/authorized_keys on the target machine needs to be 0600
d) ~/.ssh/id_{dsa,rsa} must be 0600

Hope this helps.

Accessing the remote is no problem. I already have a password protected .pub file that I had previously appended to the remote's ~/.ssh/authorized_keys file.

The problem is too much access. I added -v to the ssh line in my experiment and found that ssh lists both the key I specified on the command line with -i and the other key which is held in memory in decrypted form by ssh-agent. Then ssh ignores my stated request and chooses the one it wants.

Apparently you can only say "use this one, please", not "use this one, damnit".