I thought there was something in the code that prohibited the use of dampers for type I hoods, but I can not find anything. What I did find is the following:
From the 2012 IMC:
506.3.7 Prevention of grease accumulation in grease ducts.
Duct systems serving a Type I hood shall be constructed and installed so that grease cannot collect in any portion thereof, and the system shall slope not less than one-fourth unit vertical in 12 units horizontal (2-percent slope) toward the hood or toward a grease reservoir designed and installed in accordance with Section 506.3.7.1. Where horizontal ducts exceed 75 feet (22 860 mm) in length, the slope shall be not less than one unit vertical in 12 units horizontal (8.3 percent slope).
I remember seeing a Type I hood 5 - 10 years ago with manually operated damper plates at the exhaust points on the hood itself. The exhaust was drawn out the back of the hood and the damper plates slid in a track to cover the exhaust openings into the exhaust duct. I have no idea if that is legal or not, but that is what was provided.