Here is quite a good intro article on grease and smoke removal, grease-fires and performance of range hoods and emerging research and technologies.
As I read more, it seems the right way to go is to use a grease and smoke separation unit as a range hood (available for commercial kitchens - not yet found one for residential applications...), which does not exhaust air out of the building, saving what seems to be a lot of heat, eliminating the need for make-up air and the cost of all that ducting, control, shuttering, etc. There are now multiple strategies for removing grease and smoke from the stove plume - including filtering, centrifugal force, electrostatic precipitation (ionization), UV application, and some water spray technique. Apparently range hoods sometimes employ multiple strategies. Note dampers are not allowed in range hood exhaust systems, which means there would be a big hole in the house at all times if an exhausting range hood were installed- not at all acceptable.
In summer, all that waste heat from the stove stays inside the kitchen if the range hood does not exhaust the air to the outdoors. This is probably somewhat addressed by opening a window, if there is no AC system.