Polyison foam board applied to interior of studs

[Kismetfarmer]

I am refurbishing an old shed and am looking for some input about insulating it. The shed construction is post and beam with horizontal purlins to attach the wood board and batten siding. Rather than insulate directly in the wall cavities I was considering placing Polyiso ridgid foam board on the interior of the “studs” and nailing the wall covering overtop for a number of reasons.
1. Wind driven rain water can find itself in the cavity and would ruin fiberglass batts.
2. The foam board would provide a thermal break and stop air infiltration.
3. Cost and ease of installation.
4. The new shed would see limited use and I am not too concerned about heating it.

If I install a layer of the Polyiso directly under the beadboard would I crush the foam board as I am installing?

 

[Architorture]

If you aren't hearing it why are you using insulation at all?

 

[Kismetfarmer]

On occasions that I do use the shed and turn on the heat source without the insulation AND the air barrier/thermal break it would be 20 degrees inside when it is 20 degrees outside.

If I apply the iso directly to the interior of the exterior sheeting, there will be no air gap to allow the interior of the siding to dry. By placing the iso on the interior side of the studs I will create a 3 /2 inch air gap. The iso would then provide an air barrier, moisture barrier and thermal break.