Concerns less general contractors / trade contractors, but rather building with an architect in individual contracts, however, it may still be interesting for readers: with us, our architect always brings the contractors of the subsequent trades along during the acceptance of a trade and has them accept the work. This then eliminates later rounds of finger-pointing...
Regarding the expert, the expert we requested at the time (Association of Private Homeowners) charged between €300 and €400 per appointment, depending on the distance to the construction site and the scope of the inspection.
I would always do building with trade contractors/general contractors/main contractors with a publicly appointed and sworn expert. However, I would insist on the "publicly appointed and sworn" designation, since the term expert is not protected... you wouldn't want to end up with a self-proclaimed one.