It's because the words 'ritual' and 'religious' aren't necessarily used in the way the public conceives of these terms. I've surveyed plenty of burials which I could plausibly describe as ritual in nature. That doesn't mean people were worshipping the person/people buried there, but it does mean I think that they were making deliberate, sequenced actions to accomplish a purpose and that these steps that were culturally sanctioned/regulated.

Secondly, the division you think should exist already does. Not all archaeologists are there digging in the dirt. Depending on the nature of the site and the area, it may even be uncommon.

But here's how a typical dig site functions: the lead archaeologist/excavation director is rarely on site to dig. They're doing other things. The site supervisor/crew chief (another archeologist) manages the site day to day and does lots of paperwork, directs everyone, handles visitors, and secondarily inspects finds. These two people in consultation with others produce almost all the interpretations you dislike. Below them there will typically be some number of other archaeologists, specialists, and grad students, who may dig, but often do other things surrounding the actual digging like flotation, taking coordinates, or managing finds. At the bottom are undergrads and local workers who do most of the actual digging and other manual labor. These are rarely involved in interpretation beyond recognizing artifacts, they purely "record the facts". The laborers in particular tend to specialize in excavation. It's a point of pride to many of them that they're better excavators than most archaeologists.