Loose, breathable fabrics are great... choose brands that have SOFT blazers such as loose linen or COTTON - it doesn't have to be a structured blazer with SHOULDER pads.
Before Under Armour, the only choices you had were to WEAR a short-sleeved COTTON T-shirt in the summer or a long-sleeved cotton T-shirt in the WINTER. Why not make a BETTER piece of equipment for underneath the shoulder pads?