Do you think there is a reason Garleans can't use magic?

[Jonnycbad]

The lack of magic was a trade off for enhanced connection to machina via the third eye by either their closer ancestors, the people of Goug or further back to their more ancient Allagan ancestors.

Uh you got it backwards. The affinity for machina was to compensate for the lack of magic. The machina/magitek was something that Emet Selch bestowed and guided to the Garleans under the guise of "Solus yae Galvus". Before that, the Garleans were just a simple tribe of people without any real prowess in combat compared to Eorzean races. For all we know, Emet Selch might have created the Garlean race with the intent that they would be oppressed for centuries. Then, capitalizing on desperation, offer them powerful means to defend themselves which instantly made him their God-King "Emperor".