Not just the change in roll center height, but all the other negatives I mentioned above. You can easily lower a strut car far too much… most Mustang lowering springs!
A partial solution is to install ball joints with a longer stud to drop the control arm down a bit to correct the geometry. That can mess up the steering geometry so that bump steer becomes a problem. They sell bump steer kits for Mustangs, too. Not sure if either ball joint kits or bump steer kits are available for a Mazda 2.
Stiffer, lower springs and better dampers will go a long way to settling this car down as long as you don’t go crazy low.