I'm a builder and have considered that as well as other modifications. In short,we've learned it will not work from a practical perspective. The ideal insulation encapsulates the whole house and keeps all framing warn and dry. Now that we have double walls "down", we'll start doing exterior insulation and see how practical that actually is. (we have used the technique on retrofits)

Bob, exterior foam on double walls would require very thick foam to avoid moisture risk, since risk is determined by the ratio of R values. Are you thinking of exterior mineral wool? That would be much safer.

My proposal was to put the 2" of foam between the framed double walls, precisely for the reason of vapor issues,  As Bob I suggests above, practicality is probably the big issue unless you could easily slip the ridid sheets between the stud walls.

If you have an off-set double-wall I fail to see the benefit of foam save perhaps under the siding for radiant reflection.

http://www.rimainternational.org/index.php/myths/

I'm going with foam exterior insulation for starters and will try rock wool at some point. Rock wood board can be installed similar to foam, but adjusting it for depth is somewhat difficult and time consuming since it easily compresses much more than foam sheets. Batts would work, but you'll need framing in which to place them. Exterior blown in cellulose or rock wool, covered by a good fabric also works well, and is a tested technique, but I'm not yet convinced that this method doesn't invite colonies of living creatures to nest. Time will tell us if these methods will work for the long term.

If you are going to have double stud walls the only advantage ANY foam has is it increases the cost and reduces the "green". Cellulose, Blown in fiberglass or mineral wool are all fine insulation materials for any double stud design and cost much less than foam. Regardless of wall construction an air barrier is required.
Sheathing the outer surface of the inner wall in a double stud design can be an excellent air barrier. Usually this position of the sheathing requires a modification of the construction sequence where the outer wall is erected without sheathing, the inner wall is erected sheathed then after installing insulation the optional exterior (vapor permeable) sheathing is installed.

Would be interesting to know what the alleged "issues" are with double walls. As far as I know, if they follow good practices like "breathable to both sides, more so to the cold side", "air barrier on both sides" and "vent gap", they work well.

This guy did a decent job of it with continuous rock wool between the walls, and o.c. foam on the exterior studwall, with a slab-on-grade foundation:



He used a rainscreened siding approach, with Certainteed MemBrain vapor retarder under the drywall for better moisture control.  With the rainscreen in his US climate zone 5B location he could have skipped the vapor retarder entirely, but using air tight rigid foam instead of rock wool in the middle layer would be also sufficient vapor diffusion control in all US lower 48 locations.  But putting a variable perm

I most US locations you don't need and don't want a true vapor barrier in the stackup.  Improper placement of vapor barriers has created more problems than they have solved since widespread use began in the 1960s & 1970s.  When moisture is managed by the insulation, cladding ventilation and wall stackup rather than vapor barriers the resulting assembly is far more moisture resilient.

What climate zone are you building in?

wow all those hoops you are jumping through, i think you might want to consider ICF for your exterior walls, it will actually come out less expensive