Tire choice will likely affect mileage much more then just dropping the car 3/4".
My car is about 0.7" lower but only because my summer street tires have a diameter 1.5" smaller then OEM. I'm using 195/45R14 Toyo T1R ultra high performance tires.
The car's mileage is about the same as when I used 195/55R14 Toyo T1S tires that have the same diameter as the OEM tires.
Lowering the car will require using much stiffer springs to prevent it from bottom out the suspension. So the suspension will have less travel and the ride will be very rough and uncomfortable. The original dampers (shocks) will not be able to dampen the stiffer springs so stiffer dampers would be required for many reasons specially for safety and performance.
Maintaining a reasonable alignment will require off-center camber bolts or maybe even custom made strut tower camber plates.
I've never heard of anyone that has made these suspension upgrades to their Insight yet. These upgrades can greatly improve handling (if the parts are chosen wisely), but the ride will be extremely uncomfortable specially with the skinny OEM tires pumped up at 45+ psi for better mileage
BTW:
I don't recomend 195/45R14 tires because the ride is very stiff and uncomfortable.
But the 195/55R14 tires on the other hand are much more comfortable then the OEM tires and provide significantly more grip and performance then the OEM tires.