Moreover, just being in the general vicinity is enough for us to leave behind contamination, since humans (and all other animals) constantly shed detectable eDNA into the environment. And even if they wanted to deal with this complexity, the budget for an entire project's archaeological testing is often less than my coworkers' monthly token budgets. You might get less than a dozen radioisotope, TL, or dendro tests for the entire thing, let alone anything more expensive.