Due to our customer\'s demands, user passwords must be kept in some \"readable\" form in order to allow accounts to be converted at a later date. Unfortunately, just saving hash
One serious drawback I've not seen mentioned is the speed.
Symmetric encryption is generally much much faster than asymmetric. That's normally fine because most people account for that in their designs (SSL, for example, only uses asymmetric encryption to share the symmetric key and checking certificates). You're going to be doing asymmetric (slow) for every login, instead of cryptographic hashing (quite fast) or symmetric encryption (pretty snappy). I don't know that it will impact performance, but it could.
As a point of comparison: on my machine an AES symmetric stream cipher encryption (aes-128 cbc) yields up to 188255kB/s. That's a lot of passwords. On the same machine, the peak performance for signatures per second (probably the closest approximation to your intended operation) using DSA with a 512 bit key (no longer used to sign SSL keys) is 8916.2 operations per second. That difference is (roughly) a factor of a thousand assuming the signatures were using MD5 sized checksums. Three orders of magnitude.
This direct comparison is probably not applicable directly to your situation, but my intention was to give you an idea of the comparative algorithmic complexity.
If you have cryptographic algorithms you would prefer to use or compare and you'd like to benchmark them on your system, I suggest the 'openssl speed' command for systems that have openssl builds.
You can also probably mitigate this concern with dedicated hardware designed to accelerate public key cryptographic operations.