I'll throw my 2 cents in on this one. About 10 or so years ago, I bought a Fender Aerodyne bass in excellent used condition. It was love at first feel: light weight, very well balanced and played like butter...and it was sexy. I had to have it. But the one thing I was never happy about it was the lack of punch and sustain. I switched out the tailpiece twice, upgraded the pup’s, added a preamp, but nothing helped. Finally started doing some research on the body, which is basswood, and decided that replacing it was my last option. I bought a figured maple body (Fender licensed) and what an amazing difference it made in tone and punch, and now it has sustain for days. Sure, it’s a couple pounds heavier, but well worth it.
Basswood is used because it is cheap, and it doesn’t dull the machines and routers during manufacture like harder woods do. Why is this? Because basswood is soft…maybe a smidge harder than pine with a grain that looks like balsa wood. In all honesty, I will never buy a basswood bass again.