Can an encryption method be used as a hash function?
Provably secure cryptographic hash functions are often built using the same sort of operations as what are used in asymmetric crypto. The major problem with these constructions are that they are very inefficient. Also, a lot of these sorts of constructions have finite input domains. Thus, you have to figure out how to extend it to arbitrary length inputs.

Now, on to your specific construction. I wouldn't use it, inefficiencies aside. How do I know that you destroyed your private key? If you didn't, likely you would have a great advantage in breaking some of the properties listed above.