To be clear, leather armor existed, it just isn't attested by sources or archaeological finds to have been very prominent. But there have been a few finds, and leather can be fashioned into something that gives some light protection. Actual prominence in use is debatable, but there is nothing implausible about leather for a fantasy armor.
Studded leather, however, does not seem to have ever been a thing, and, as imagined, does not seem to be capable of providing any additional meaningful protection over leather without some studs in it. Studs are usually portrayed as too widely spaced to do anything meaningful, and were they tightly spaced they would provide less protection for more work and resources than attaching larger pieces of metal. Some people believe that, as portrayed, studded leather seems to be based on misinterpreting leather brigantines with the leather on the outside and plates riveted to it on the inside as just leather with studs on it, which would seem to suggest leather brigantine as the logical substitution.
But leather brigantine is AC 13 + Dex medium armor in this system, whereas padded leather is AC 12 + Dex light armor, which would seem to occupy the space of studded leather, with leather's old place given over to padded cloth, which, unlike in 5e, actually gets to have a distinct identity (comparable to that it had in the middle ages) as the basic, workhorse every day light armor, rather than just being offbrand leather armor.
