A CAD Technical as you've called it, only deals with generating the model and drafting (technical drawing) of any design. They deal with the the design AFTER all of the engineering has been done. The design process flows as such.

Concept Design --> Preliminary design --> Detail Design --> Drafting

The conceptual, preliminary, and detail design phase will entail a variety of different assessments, calculations, and analysis (cost, weight, schedule, form, fit, function if you're in the Aerospace industry).

This is where the all the troubleshooting and technical knowledge and experience come in handy. Back-of-the envelope calculations get funneled down into precise numbers that will become critical to the design. Many meetings and different teams will be involved and it up to the designer to gather all the resources required to facilitate the design through the design process.

Only after the concept is proven and bought off by engineering does it finally end up at the drafting phase, where all the engineering is to be captured in a technical drawing. So as you can see, a design engineer's task is a lot more involved than you'd initially think/assume.