You are correct that sympathetic stimulation of bronchial smooth muscle causes relaxation, which allows for increased air exchange. Stimulation of the beta-2 receptors causes the smooth muscles to relax in the bronchioles and also in the intestines, blood vessels, uterus, and bladder. All of these actions are consistent with the idea that the sympathetic nervous system prepares us against threats. We need oxygen and blood flow, not digestion or urination (although some individuals do seem to find a way to urinate even with the sympathetic relaxation of the bladder).
As Newtonian21 mentioned, bronchodilators help improve gas exchange and increase oxygenation. Bronchodilators (like albuterol) are beta-2 agonists that stimulate the bronchial smooth muscle to relax.