How plausible it is to lack access to common resources in medieval time?

That is a clear definition of resources.

If you look at AoE, you see that there are various ways for gathering food. The main resource group is food. Yet the player gathers grain, berries, livestock, wild animals and fish.

What most games lack, is a logical distribution of the resource classes, when it comes down to spending the resources.

I always think that having different resources becomes obsolete. When all the things that a player can buy has a mixed costs. Or you can exchange one for another.
You see this in older games like Warcraft123 and of course AoE.

Then it is a simple matter of having the need for the most expensive resource. Or the resource that is the most abundance.
The other resources are simply there without function, except for a thematic idea on what the player wants. A wooden carriage costs mainly wood, idea.

So, if you design a game with different resources. Then you need to add extremes. The wooden carriage ONLY costs wood. This way, if wood is depleted. You cannot get those wooden carriages anymore.

Now we get to the point of having either a wooden carriage or one made of metal. And this is where I stopped using different resources in most of my games. In fact, even my Starcraft maps made use of only 1 resource. The other one either was being processed in the main one. Or it was a tech level that player had. Ah yes... I now remember my unfinished RPG map in SC.

Either way. If you design a wargame. Or other games with different resources. Each resource needs to be functional. And it can even be abstract.
If it is depleted, the player needs to have a problem.
It took a long time for me to realize this.

***

2015 to present.
My prototype has (or had) these:
- XP, used for having stronger variants. It was an upgrade resource, adding an extra layer to the choices. And had to be earned through combat. Could be used only on themselves. Later on the distribution was global through a centre.
- €, used as resource. Just limited enough that a player had to make a choice of what units wheren't build yet.
- SP, used for (balancing) extra actions. Provided by "bad" designs. Could be used only on themselves. Later on the distribution was global.
- AP, used for actions. Simply to futher limit the player.

Completely(?) different than your goal, I know. But here you see, every abstract resource has its own function.

***

Let's make it more in your direction now.

Somehwere around 2000.
Once I tried to copy Warcraft, but had not need for gold. And material could be damaged as well:
- A person, costed 1 person.
- Wood, you had the wood attribute to armor or weapons.
- Iron(Ore), you had the ore attribute to armor or weapons.
- Oil, you had the "oil" attribute to armor or weapons.
The resources used gave attributes to the units.

Wood could easily burn by weapons that used oil. Still it added armor to an unit.
It was also the basis to most weapons.
Iron simply added much more armor as substraction... Well, any damage was reduced by/to a percentage, this was a mechanical RPS effect. Processing iron could also cost wood or oil, depending on how much you needed.
Oil could be used instead of wood for burning processes.
I could go on and on about this. But let's say that each next resource was more expensive. And with 2 steps, it would already be overkill. Iron weapons on soldiers without armor was overkill.

The oil had an upgrading effect. It made the weapons more specialized. Read this as, the disadvantage gap simply got bigger as well.

***

2008 to 2012.
WargameX
Nostalgia, copypasta.

- Carbon, it’s main use is for low armored units like infantry and some vehicles. Carbon in pure form is black.
- Metal is used for medium armored units like vehicles and tanks. It is also used for medium ranged units. Due to the compositions of the metals it’s average color is blue.
- Xtreemium (don't ask) is used for high energy weapons which fire a lot of times in 1 turn or do a lot of damage in general. It is also used for the really fast units. This super energetic and radiating substance is brightening white.
- Hyperotonium is used for highly armored units and units which fire across long distances. This super metal has the color orange.

10 years later, yeah, maybe the naming could have done so much better. This was certainly before I went into carbage disposal. But also before I met you all on this forum.

I devised a complex calculation mechanic for myself. In order to determine how many resources you need of each. But while each resrouce touched the function of the units. This game, AND the medival game, both had the disadvantage that I mentioned before.
If resources where abundant, there was no use for the differences.
It really boiled down to: Have special unit A or B? It wasn't a matter of having the choice of unit from the whole alphabet.

That is also why, knights and ogres are produced instead of footmen and orc's. The first are relatively cheaper.