Most U.S. building codes require at least some site visits by the engineer of record.
Also, the TRUE purpose of requiring shop drawings are twofold:
1. Forces the contractor to develop exact plans of the individual pieces and the erection of your structural elements. This aids the fabricators and streamlines the fabrication process. It also makes the contractor really "get into" the project and in the process, many issues of construction, means & methods, and scheduling appear, helping the contractor to do the job better.
2. Allows the engineer of record one method of determining IF the contractor is correctly INTERPRETING the design plans. Your plans and specs are a communication tool, and the shop drawing reviews permit a check on whether you are adequately communicating.
A third party reviewer can satisfy item 2 above IF that reviewer does indeed understand your plans. But there are always subtleties in any design and the engineer of record can do it best.
This same item (2 above) is achieved by the on-site observations. You look for general conformance to your design plans....not to check/inspect every little piece of work for conformance....but to verify that the contractor can indeed properly interpret your plans.
In other words, if they get a sequence of rebar placed properly in one place, they therefore have the ability to properly get it right in all the other places of similar condition.
So a third party reviewer or on-site observer must be able to interpret your plans to do this job right. How do you know that they can do this?