What is the harm if I publish an encrypted RSA private key publicly?
Systems like ssh, for example, often encrypt a user's private key using a password, so that is not new. The fact that they are published on a web server that technically anyone could access is a little different. But, if the password is strong, brute force and dictionary attacks would be impossible. So the system seems secure.

That if, though, is a big if. As CodesInChaos points out, users are bad at picking good passwords. So, lets assume they are still bad at picking passwords. Eventually the URLs will become known, so we can't rely on that for security. An attacker can then download the encrypted private keys and decrypt them since a bad password was chosen. 

How does this differ from traditional passwords? Well, in traditional passwords, at least the database and server can be hardened to keep people from getting material that can be used in an offline dictionary attack. Under this system, the URL scheme would be the only thing preventing an offline dictionary attack.