A Plascore-based sandwich panel constructed with two layers of 3k carbon (skins) and a 4” thick (5 PPCF) core material is 50 Times stiffer than four layers of 3k carbon, alone. A sandwich panel with this same core and skin combination, but using an 8” core instead of a 4" thick core, is 180 Times stiffer than the skins alone. Weight increases by 33% going from solid skins to a 4” core and 60% (total) over the skins alone. This is a small price (in weight) to pay for the massive rigidity, impact absorption and load-spreading capabilities of a sandwich panel.
In any sandwich panel design, the skins carry tensile (30-42 ksi for 5086) and compressive loads (10M PSI for 5086), while the core carries the shear load (1600 – 2200 PSI for quality Structural foams, honeycombs, etc). So, you want a thick core (taller I-Beam) with high shear strength and skins that have high tensile and compressive strength. This is why EPS and XPS make terrible choices for a core material, regardless of your skin choice.
If these foams are chosen for their insulation properties, one must either build a robust "exo-cage" to carry the loads or have massively thick skins to do so. In either case, you have lost many/most of the benefits of the sandwich panel design. Further, I would contend that you don't have a sandwich panel at all. You simply have an insulated wall, just as you do in a house.
Can you build a 6' x 8' tear drop trailer using EPS, old bed sheets, and Elmer's glue? Sure. Go right ahead. That is one way to build a SIP/sandwich panel, but certainly not the right way or the best way, to do so.
Choose the best materials you can afford and do it right, once. If you cannot afford good quality products, you likely should not be building, as doing it 'upside-down-and-backwards' just finances the negative cash-flow over a long period of time.