I think the easiest way to resolve this is:
a) Remember that we're talking about functional plate suitable for wearing into caves, sewers and swamps, not ornate ceremonial dress plate. So a lot of the factors that could make plate expensive do not apply. Sure, you could get someone to do all the extra work on a set of armour to make it worthy of ceremonial wear, but the sets we're talking about don't have all that. In the PoL setting, that level of craftsman turns their attention to Dwarven Plate or Godplate.
Speaking of PoL,
b) The setting assumes an empire that collapsed only a few generations ago. That suggests lots and lots of military 'surplus' was collected either by the honorably discharged, deserters, battlefield scavengers, the enemy etc. This would include a fair amount of mass-produced plate - the sort that could be easily resized to fit members of a large army. A blacksmith could probably alter a set to fit someone similar to how they alter a horseshoe. It may have taken a month, but that's just backstory unless a PC wants to upgrade to a nonmagical set of plate during play.
because
c) Remember that the 100g starting wealth is the value of the starting gear - the PC does not walk into a shop in their underwear with 100g to spend.
Finally,
d) Plate does not offer significantly better protection than scale, and has stiffer penalties, to the point that there is some argument as to whether the extra point of AC is in fact worth it. So it doesn't make sense to try and charge too much more for it. Not only is it unbalanced from a game design point of view, but there wouldn't be many NPCs willing to spend 20 to 30 times as much for something that had as many drawbacks as benefits.
So it makes sense for a functional, utilitarian set of plate to not cost much more than a set of scale.