Here's my unofficial take on the matter.

For years, T-1 was the South Terminal. T-3 was the North Terminal. T-2, pre-closure and reconstruction was the old International Terminal (and was to be again the Central Terminal). The new International Terminal opened (containing the A and G piers, and the only piers in the airport where the gate # has an associated letter). Note - no gate number is ever repeated in this airport, except some gates will have an A and B component. After this time, South and North were renumbered 1 and 3.

It appears that the "master plan" would have been for each gate to have a pier letter and then number component, as the piers are all lettered, i.e., the AS gates are all in B, and numbered 20, 22 and 24. This has not occurred, and it really isn't necessary because no gate numbers are repeated, and there already is some logic (i.e., A has 1 through teens, B has 20s and 30s, C has 40s, D has 50s, E/F 60-90 (all behind common security), G has 91-end.

So, "I" was given its "code" designator (in GDS systems, not the airport's doing) when it could only be "confused" with North and South.

Just my observations.