I think it is incorrect to say that Rap and the low cost of recording drum machines and turntables "killed" Funk.
If that's the case, why didn't cheap electronics "kill" any other genre of popular music? Rock, blues, jazz, classical, etc. That was the fear when samplers and midi came out. But guess what, they just became another too for making music. Rap is it's own genre which definitely evolved out of funk soul and rock.
When I was young a lot of funk got incorrectly labeled as disco. I think this hurt funk. I also think that what is commonly known as funk (the hits) became too narrow of a genre. But what do I know, 1 4 5 blues just keeps chugging away somehow. I do think it's true that it just may not be in the forefront of music right now.
I love Funk music, it just makes me feel great to hear it. I wish I could play it better. I am pulling for a big Funk comeback!