CHICAGO—President Trump’s promises to reverse the regulatory actions of the Obama administration have been stymied by court challenges, but his administration is achieving the goal another way: by not hiring people to do the work of enforcing rules that are on the books.

At the Environmental Protection Agency, where staffing has fallen to Reagan-era levels, there were 10,600 inspections last fiscal year, down from nearly 21,300 at the height of President Obama’s second term, and less than 60% of the annual average since 2001....