Militia can't use plate armor?

[Claytonium]

Well, that was a wasted development point...

[pckirk]

What level are your burgages ?

Militia are units recruited from among the male villagers. They require weapons depending on the militia type. Each militia is made up of 36 men but can have less if there aren't sufficient weapons. Each soldier will try to equip a Helmet if one is available. If their Burgage Plot is level 2 they will also try to equip a Gambeson if one is available, while level 3 Burgage Plots will request a Mail Armor instead. The helmet and body armor are both optional for a troop to form, but both increase the armor of the troop. There are 4 militia types:

[Didz]

Plate Armour is only worn by the Men-At-Arms of your Retinue. So, making it yourself saves 34 silver per man (816 silver for a full unit) in equipment cost.

[beersmurff]

Not wasted. You learned something. Not only about the game but history. Militia didnt use Plate Armor. They often used no armor or had some left over inherited old gambeson or chain from their fathers father etc. A sword and plate would cost as much as a medium sized homestead back then. Farmers and peasantry did not have that money.
Some richer nobles would help equip the milita, but again, providing shields, gambesons and some halberds etc. Not plate. If a peasant stole a plate armor after a battle he would have to hand it to the noble or be flogged. If he got away with it he might try go the Hedge Knight route but that was mostly for professional soldiers and not an untrained farmer.

[Didz]

A full suit of Milanese Plate Armour would cost a Knight the approximate equivalent of a Ferrari Sports Car today. It was not in the price range of a peasant, and not many knights could afford it either. Most of the French knights at Agincourt were wearing grandad's old cast offs which is why the English arrows killed so many of them. It wasn't until the French King hired Milanese mercenary knights in the latest kit that the English got their comeuppance.

[Marius]

A full suit of plate is too expensive for your citizens, yes (our Lord could wear one, though...), but a simple breast plate (even if without the back to make it even cheaper) is absolutely fitting for a militia of a decently sized town. At Lv3 does militia men are probably pretty rich artisans. (And, btw, depending were you are, a breast plate is cheaper than a mail shirt. It can be produced a lot faster)
In some cities it was REQUIRED to have at least a half suit of plate armour for artisans. Those werent poor peasants. And even farmers probably could afford a decent set of armour. If you own a farm you are not poor.
It all depends on the time and place, of course.