Adding software obfuscation to the standard white-box designs is close to what it is already done in the industry. This solution is not strong enough, it can be somewhat useful to make reverse engineering harder and make the attacker spend a longer time to fully understand the underlying design but does not avoid the key extraction. Software obfuscation, indeed, makes harder to understand and potentially lift some portion of the code but does not avoid the execution of the encryption function. Few years ago, a new family of attack techniques, borrowed from the secure element world, has been successfully applied to the white-box context (see Differential Computational Analysis(video here), Differential Fault Analysis, shameless plug: Bucketing Attack). With those more recent techniques, even if the software is obfuscated the attacks are effective.
On the other hand, code obfuscation aims to hide the logic of the obfuscated algorithm, and usually, this is not the same security target of such situation you described, code obfuscation aims to hide that the obfuscated code is an AES implementation, but from a security point of view, the attacker already knows the encryption algorithm, only the secret key has to be protected. Code obfuscation in this context is used to hide how it is computed and in particular when/where the key is loaded in memory, data obfuscation is used to hide the link between some loaded data and the plain AES key.
If you are looking for white-box designs you can have a look here: Side-Channel Marvels (more specifically in Deadpool) or OpenWhiteBox.
actually the scientific community and the industrial one are actively looking for a better idea and solution to the problem. The industrial world is looking for a secure enough solution staying secure for the life of the product (at least until next update).
As today no know design is considered secure, and as a consequence the industry produces software security solutions including (but not limited) to white-box cryptography, anti-tampering and anti-reverse engineering techniques, but to keep an advantage over the attacker the details are not public.
Some other (non published) designs are available at the WhibOx Contest - Edition 2