Firstly, I find it hard to believe that Aang simply lacked the aptitude.
When Toph first discovered Metalbending it was established as being directly related to her seismic sense; she used this to detect the impurities in the iron before she was able to manipulate metal using Earthbending. In other words if you can sense those impurities you can learn Metalbending. This is enforced by Suyin Beifong(a Master Metalbender in her own right) who believes the only true barriers to an Earthbender learning Metalbending are self-imposed.
As Aang masters seismic sense to the extent of training blindfolded against both Toph and Katara and intercepting Ozai's attempted surprise attack in the final battle it stands to reason he could, in fact, learn Metal Bending were he to train under Toph.
If it were something to do with heritage then Korra, who is Water Tribe, couldn't possibly have a trait unique to the Earth Kingdom any more than Aang could.
I know some people will argue that Earth being Air's opposite is the reason Aang simply can't learn an advanced Earth Bending technique, but aside from repeating myself about seismic sense I think it's important to understand this is only a difficulty in learning curve that is faced by most Avatar's due to starting out in learning their own cultures bending independently. Korra proves this cultural basis of learning difficulty by learning Earth and Firebending at an unprecedented age and having no aversion or weakness towards Firebending. She subsequently has the most difficulty with Airbending.
Furthermore, after overcoming his initial difficulties Aang picks up Earthbending at a phenomenal rate, his mental block having no further influence on his learning.
I suspect that at first Aang was busy with settling matters throughout the world after a century of war, including the establishment of Republic City. After that he probably wanted to settle down with Katara and then pass on Air Nomad culture and bending to Tenzin. Similar to Roku he reached a point in life where his own family became a priority. The reality is that with 4 elements Mastered as well as Energy Bending he is extremely powerful without Metal Bending. Aang achieved a huge amount in a short time and chose to rest rather than chase every conceivable aspect of Bending. As Iroh said to Aang under Ba Sing Se; 'Protection and power are overrated. I think you are very wise to choose happiness and love...'