How important is the quality of passive crossovers?

I have a pair of Yamaha 7390 3way towers layin around. They are all that you can expect from sub $200 towers, boomy, no mids, screechy highs.

Having accidentally landed on this board, my DIY loudspeaker interest was sparked. Being a total newbie, swapping out the woofers and the midrange cones would be a fun thing to do as a 1st attempt thing imo.

Having looked through some other threads regarding refurbing commercial speakers, a lot of people seem to advise against it, and recommend starting with a premade housing. Thing is though, I have nothing to do with the 7390's lol, they were in my basement for ages now, no one wants them, and I dont want to throw them out. My refurbing results do not have to be spectacular, but obviously I want to gain at least something quality wise out of this procedure other than just the expirience.

So my question is, should I also swap out the the crossover, or should I leave the old one in place?

Also any recomendations for cheapish but half decent 6" - 6" 1/2 (16cm) woofers, and 4" (10cm) midrange cones? Preferably in the ~$30 range each.
 
You can just swap out the drivers, but its really a crapshoot whether it will sound any better unless you also design a new crossover for the new drivers, especially since you will be limited to drivers that will fit the existing cutouts.

Basically if you think this woudl be a fun way to spend a little $$$ to get your feet wet in DIY audio, and learn a few things in the process, its a great idea. If you are looking to improve the sound of these speakers, and will feel like you've wasted money if you fail to do so, or end up with worse sounding speakers, then its not a great way to proceed.