Tatra 57 at the Josefuv Dul Car Show, Liberecky kraj, Bohemia(CZ), 2015

Here's a much better look at the grilless front end of the Tatra 57. Although this design was changed for the 1937 model year (Tatra 57's stayed in production until 1949), the initial omission was probably down to the 1932-1936 Tatra 57's 1155cc flat-4 engine, that like many flat or "boxer" engines, was air cooled. Presumably, the grille was added from 1937 onwards because air-cooled engines can still benefit from the improved airflow that a grille provides, even if there isn't a radiator. For a comparison, think of a laptop, and the need to provide adequate airflow. Generally, laptops with a lot of grilles should cool better than ones that don't have any ventilation (and we all know which manufacturers I'm referring to).