[Question] Why aren’t we testing general intelligence distribution?

IQ sup­pos­edly mea­sures gen­eral in­tel­li­gence. As­sum­ing the g-fac­tor ex­ists, why are we us­ing IQ to mea­sure it? IQ tests get tweaked so the end re­sult will always form a nor­mal dis­tri­bu­tion. I checked wikipe­dia to figure out why, but while it said some peo­ple claim that LCT is a good rea­son to be­lieve the g-fac­tor will have a nor­mal dis­tri­bu­tion, it didn’t seem ter­ribly con­fi­dent (and it also didn’t give a source). Even “The Bell Curve” used an in­tel­li­gence test that didn’t re­turn a bell curve at all. They said they had to turn it into a bell curve to pre­vent ‘skew’:



But isn’t this putting the cart be­fore the horse? Surely it would be in­ter­est­ing to see what dis­tri­bu­tions we would get if we did in­tel­li­gence test­ing with­out a re­sult in mind? I get that it is re­ally difficult to mea­sure, but if a test con­sis­tently gave us a differ­ent dis­tri­bu­tion, we could learn valuable in­sights into how hu­man minds work. So is there a rea­son why we aren’t test­ing the hy­poth­e­sis that gen­eral in­tel­li­gence will fol­low a nor­mal dis­tri­bu­tion?