I apologize for not responding early, but I was on travel last week and had little time to respond.
Generally, the predominant reasons for alloying a metal are to increase strength, hardness, and resistance to wear, creep, stress relaxation and fatigue.
The low strength of pure Al limits is commercial usefulness, so it is alloyed. The tensile yield strength of high-purity Al is about 10 MPa (~1.5 ksi) while some heat-treated commercial high strength alloys have yield strengths greater than 550 MPa (80 ksi).
With respect to 'non-heat treatable' Al alloys, by definition, these are alloys that do not realize an appreciable increase in strength with heat treatment, and this is primarily because these alloys do not experience precipitation hardening. This is related to their composition.
The non-mechanical strengthening mechanisms which apply to non-heat treatable alloys include solid solution formation, second phase precipation and dispersoid precipation.
Otherwise, strain hardening can be used to increase strength in non-heat treatable.
By contrast, heat-treatable Al alloys are those alloys which do realize an appreciable increase in strength when the suitable heat treatment is applied.
There is a very good article on Aluminum and Aluminum alloys in the Metals Handbook published by ASM International.
According to the article, the elements Mg, Si, Zn, Cr or Mn alone contribute little to increased strength with thermal treatments. On the other hand, Al-Cu alloys with more than 3% Cu exhibit a natural aging after solution heat treatment and quenching. This Al-Cu system is the basis of the 2xxx series of Al alloys.