What is everyone's opinion on an attic that is insulated on the underside of the sheathing instead of over the bottom cord of the trusses? And making the attic air-tight. Resulting in the attic being climate controlled just like the living space.

I have advocated this system, and used it exclusively, for the last 4-5 years. It works very well in our climate, and the advantages far outweigh any perceived problems.

What about Minnesota's climate? Can give me some details, I don't know much about the system?

Love mine in Florida.

I would think that in an extreme cold climate the advantage of not having every single ceiling and top plate penetration chimneying warm air up out of the living envelope would be huge.

Sealing the ceiling isn't much of an issue, I would have urethane sprayed on top of it. Attics are how we, in the north-land, deal with condensation. Warm moist air that gets into the attic gets vented out. But if no warm moist air escapes, we shouldn't need the space, right?

But how about in the summer, with a hot roof, the venting keeps the top of the insulation cooler? Not so in a sealed attic or SIP roof structure. It must cause the roof to get even hotter resulting in a shorter life for asphalt shingles, more expansion and contraction with any roofing.

the idea of venting the roof to keep to keep it cooler is an outdated and ineffective approach.  You may get a slight decrease in temperature by have a 'working' attic ventilation system, but the color/shade of the roof would have a much larger effect on it.  A lighter color roof can be as much as 50 degrees cooler then a darker roof of the same material.