The problem with that is that under GDPR you have to support full deletion of an user's data.
You can access your customer data, using the customer-specific AES key. You can access the customer-specific AES key using your private RSA key.
When you need to delete the customer data under GDPR, you can delete the encrypted AES key for that customer from your database.
Now you have the worst of both worlds. You also now have 2 points of failure where data can get lost, because if either has a problem you lose data.