Yes and no. There is no issue with the leaf and handling. However, the leaf spring rates were chosen as a compromise between ride and handling. If you want sharper handling you may need a stiffer spring. There are only a few options for replacement leaves. If none have the spring rate you want then you have to go coil over. The leaf would be replaced for the same reason the coils on a Miata would be replaced to improve handling.
The other part of the equation which is really the big part is replacing OEM dampers with far more expensive aftermarket units. OEM dampers are almost always a compromise (the mag dampers are perhaps an exception) between cost, supplier certification, etc. Also with the OEM dampers again you get what the manufacture considered the best trade off not necessarily what YOU think is the best ride handling cost trade off.
So yes, you may end up with better handling with coil overs but you likely would get that same better handling if you could get the aftermarket damper and an equivalent rate leaf spring.