38Super,
I was not aware of the Thermobuilt System.  Thank you for posting the web site.  I just now watched the video and read some of the tabs.  Because of the EPS, I think this system is better than stick built with fiberglass.  However, I do have one question.  The roof appears to have thermal paths at every support (I-Joist).  Would additional insulation under the drywall be required to insulate the I-Joists?  Also, my guess is that the R-value quoted on this site is not whole wall.  Although I liked the air flow under the metal roof that was created by the I-Joists, roof decking would be required for shingles.

Interesting system, looks well suited for a kit. I wonder how well it works for a custom. I would use foam to foam spray everywhere.

My only 2 reservation are the wood framing and they recommend stuccoing right over the insulated framing with no sheathing or house wrap. Also, no vapor barrier behind the interior wall board. They say the EPS foam is a good enough vapor barrier. It may be.

I have a link on my home computer for a type of composite lumber used for framing. It's termite proof, fire resistant and stronger than wood. I think it's also straighter and more consistent.

I'd also prefer to sheath the structure, probably with MgO board, cover that with house wrap and a vented rainscreen made of corrugated metal.

Primary goals of this method, (besides excellent insulation), would be termite, mold and fire resistance.

This was a system developed in the southern US, and most of the installed base is in the southern US & Cayman islands.  In those climates if vapor-retarders are used they need to be on the exterior, not interior.  I suspect this system works just fine as-is in most of FL and the gulf coast states, but may have issues in very high rainfall areas.

EPS is highly permeable compared to XPS or foil-faced ISO, etc..  But while not a vapor barrier in thin layers, at 8" the permeability is always under 1 perm making it a class-II vapor retarder.  (Some EPS would even achieve class-I at that thickness, but not all.)  Still that's good enough for most of the lower 48. Sealing the seams with foam or mastic is a good idea though.

I too have some reservations about highly-wettable stucco applied directly to the EPS (particularly in the tropics!).  EPS is very hydrophobic, but even at sub-1 perm the latent-load to the interior could be raised using stucco without a drain-plane & rainscreen/cavity.  Moisture that reached the studs would be easily wicked toward the interior.  It wouldn't be tough to re-engineer the system a bit, add housewrap held in place by a furring strips on the studs to form a drain plane & cavity/rainscreen behind the siding layer, but without sheathing there may be fire-spread issues with the EPS if there's a gap or rainscreen.  (Which is perhaps why they went with directly applied stucco as a cost saver.)

In the most-humid areas the include whole-house fan isn't a real winner either.  Even at night, sucking in un-treated outside air will raise the latent load much of the time, even as it brings the temperature down.  Some amount of active cooling/dehumidification may be preferable.  (Even if your structural lumber is mold-free, that doesn't mean your cabinets, flooring, or furniture will be.)

In cold climates you'd still want to apply vapor-retarder to the the interior surface (vr paints, if not foil-faced isoboard or poly sheeting ), even if the structural lumber is rot-resistant. The permeability of the inch or so of EPS out to the framing is NOT a class-II vapor, and frost-formation could potentially increase the gap between the framing & EPS over time, degrading the performance somewhat.