Adobe vs cob: a framing question

The short question: Can I use adobe bricks instead of wood to frame a cob dwelling?

The longer version:
We'd like to build a home  that is
1. Suited to our environment, which is a high desert juniper/pinion forest. ~17" precipitation/ year, mostly received as intensely heavy downpours during the summer. Temps averaging mid to upper 90F, to 20F. Spring winds between 20-50 mph.
2. Built with mostly on-site materials and hand tools. Rocks, clay, wood (not lumber), some course sand and grasses are available.
3. Tailored to our bodies and habits. (No manufactured homes or cookie-cutter one-size-fits-all plans.)

We have considered domes, storage containers, cob, adobe brick, cordwood, and rock (slipform) designs. I really like cob, but I really dislike having to build a stick frame for it. Adobe seems like the next closest product, but since I am not a mason, I worry about a self-made dwelling being sturdy and safe... I also crave the freedom to curve walls, which is not a common feature of brick buildings. So I'm wodering if I can frame a building with adobe and fill with cob, cutting our lumber use to just overheads and bond beams. Is that a dumb idea?
There are many examples of very old adobe dwellings in the southwest, but no cob. I wonder why, since they are essentially the same materials in different formats.

There really isn't any need to frame a cob house, it can easily bear the weight of a roof by itself without framing adobe or wood. You would end up having a much stronger structure with a purely cob structure--well designed and well built--than with a frame in job.

One of the strongest parts of a cob house is the fact that it is monolithic in nature. The walls are essentially one wall. Once you start making pillars of other material and infilling, your strong wall became many walls separated from each other.

Many cob structures that have implemented post and beam do so to fit codes or to provide a roof shelter for building under and protecting the cob. Both are great reasons to use post and beam construction. It all depends on your available materials, your local codes, and what you feel comfortable doing.

Ahh! Of course. I kept hearing how straightforward cob building was, but while researching in published books I found more and more caveats... No one wants to publish without an effort to include building codes.  Thanks for the nudge, Daniel.