The shroud could actually act as a limiter when too much air tries to enter through the radiator.
Some shrouds have rubber flaps that open up when enough airflow is there.

Also most likely that underhood air can't escape the engine bay fast enough causing lower airflow through the radiator and engine heat is building up.

A front spoiler can create some lower pressure behind it which could in turn help evacuate hot underhood air and aid overal cooling.