Are there good free software analog filter design tools? If not, why?
There are a number of online tools though they are often limited.
Here is a list of online and free desktop tools

Active filter web based tools


TI WebBench Filters
Analog Devices Filter Wizard


Active filter desktop design tools


FilterLab by Microchip
FilterFree from nuHerts
FilterCAD3 from Linear Technologies (Now Analog Devices) Though official links to original sources of it seem to have vanished.
FilterPro by TI
FilterWiz Lite by Schematica


Passive filters


AADE Filter Design tool by KE5FX (Ham radio)


Simulation

I would always recommend simulating the software generated filter with real life simulation models of the components you intend to use for your implementation.

Use a different simulation tool that the generation tool to limit the possibility of software bugs effecting your design.

If you are not dealing with purely sinusoidal signals remember to consider the step and impulse response.