True, it was removed from the National Register of Historic Places, due to the addition of the modern seating bowl. However, that doesn't mean that the stadium is no longer historic in its own right. The construction of the bowl affected the interior of the stadium, while the exterior still boasts the original 1920's limestone facade and the monumental Doric columns/colonnades.
While the modern addition has been decried as awful and badly clashing with the stadium's neoclassical design, the original seating was pretty bad. The angle of the seating was too low, and you were too far from the field from most vantages. The fan experience has definitely improved with the addition, despite its odd "UFO landed in the Parthenon" look from the outside. Not adding a dome was probably the biggest mistake of the addition, although they honestly should have looked to build a completely new stadium somewhere else in the city instead of pushing for this poorly thought out expansion.
Regardless, at the end of the day the Bears moving won't diminish the stadium's use all that much. It hosts many other activities, including a Major League Soccer franchise which hosts more than twice the home games than the Bears do, so its far from being a white elephant. Let the Bears move to the boonies.