Practical filter found in better speakers use both approaches simultaneously

The worst speakers just have a cap to not blow the tweeter and drive the bass/mid full range and hopes for it's natural roll off to be ok enough ?
I would get software if i was into DIY no one misses all the calculations , let a software do it for you . It's no a to complicated circuit when the design is ready you can buy separate components instead of this ready made filter and follow the schematics and assemble it yourself .
I have not tried in decades but todays software should support using the actual impedance curve or equivalent circuit of the drivers ? I have no recent experience sorry