Possible to do full wall paneling in modern construction?
Yes, it can be , and is done all the time. We use to call this style "craftsman style." All the elements you describe are included in that style: hand made paneling, open beam construction, you say, "lattice type " ceiling (we call coffered ceiling), etc. 

Now we use these elements in our designs for upper end projects, (just like they did in the craftsman style, which most people don't realize). When we are trying to do something special, we'll often add wood details.  However, this is only economically feasible for the most custom and most expensive construction. 

Yes, as others have stated, the cost is too prohibitive for most homes...both labor and material costs. Our housing market has changed.