Is asymmetric encryption ever recommended for long-term storage of data, is it advisable for example to store data in a database such that:
1) A user enters data on a website, it is encrypted using a public key and stored. Neither the webserver nor the database server stores the private key.
2) The data is downloaded by a worker who was the permission to access it.
3) The worker uses the private key stored on his/her local computer to decrypt the data.
Assuming that the worker's computer is free of malware, the seeming advantage would be that if the database server were to be compromised the data would not be accessible.
What would be the problems with doing this?