Sonic Youth didn't really steal from Branca... They learned from him. As in Thurston took lessons with him when he moved to NYC and Lee actually played in Branca's ensembles even during Sonic Youth's early years. So saying they stole from him isn't really accurate... it is like saying The Breeders stole from the Pixies.
To the original poster though, I own multiple guitars (all electric) so that I can leave them in different tunings, leave them in different rooms and (the most legitimate reason) because they sound differently. I play my american tele the most because it is my favorite guitar ever and covers just about everything I like to do to some extent. Then I have my ibanez Talman for those times I want to play around with a whammy bar, it also helps that this guitar is seafoam green with a pearloid pick guard. Then there is the Squier Super Sonic that is just a total piece of shit that I keep meaning to paint purple and drop new electronics into it and give it a short scale neck... right now it just sits on my sofa in the classic "Pavement tuning" DADABE. I just bought a 1960's Univox ES-335 clone that is pretty sweet but needs some pots replaced. I will probably find some peaceful uses for it, but right now it lets me pretend like I am in the Jesus and Mary Chain while pissing off my neighbor.
So there isn't really a great reason to have more than one... a lot of people can't tell the difference between the sound of a fender style single coil/P90/humbucker, and a lot of the draw is definitely based on the guitar's appearance (some of them just look too cool to pass up, if not for the price tag I would 20 Jazzmasters for this reason alone). But having a guitar for every room, or a guitar for every tuning you like are the most common excuses I use. I used to try and explain the difference in their sounds, but that just led to more questions like "why do you have so many fuzz pedals?" and "why did you pay $200 for this delay pedal that only has 600ms of delay time while this other one costs $70 and has 2000ms of delay time?" (the classic analog vs. digital debate).