Neither has it ever been suggested that they can't.
To me, the real reason they bar scholars from it is because it's the most lazy way out. Emerald Carbuncle already exists and has the exact same abilities as Garuda-Egi, so there's no additional work here, abilities all have fitting animations already. Same for Topaz and Titan. Ruby Carbuncle is already in the game as well and I doubt it will have any "new" animations but rather take from Topaz Carbuncle animations. Pretty sure that you can't make Garuda a Topaz or Ruby Carbuncle either, because that would be additional work.
