Kinda hard to continue as a band after your vocalist is murdered.
Well yes, but a band desperate enough could continue with a new lead singer. Nirvana was not desperate, obviously...and not that anyone would have wanted Nirvana to get a new lead singer, that would have been insanely stupid. But there was technichally a breakup. Call it whatever you like.
And about the whole murder vs. suicide thing...I will NEVER claim that I know for sure, and I think it's silly that anyone says they know for a fact that he was killed...(not saying that's what you're doing, you just mentioned it, which sparked my tangent...) Personally, I highly doubt Courtney killed him, but that's just an opinion, because everything I know I learned from the internet. Not exactly the most reliable source.