This is really annoying. I don't and haven't ever used vine, but how much could it really cost to keep hosting it, and let people continue using it? Why can't companies be okay having products that are revenue neutral that make people happy?
If you kill it because it costs something and you have no plan to ever keep it going, people complain
If you let it live but just "keep it working", people also complain.
Additionally, killing it brings certain nice guarantees, like, for example, "you can stop worrying about security bugs, privacy bugs, etc at some point" because it's gone.
You can't really just keep stuff working anymore, even in the simple case, new attacks get found that apply to old code, etc.
When those things get busted, or bad things happen, people complain about it.
As for "why not just put one person on it", there's a multitude of reasons. Let's start with "what is the career path for a guy who does nothing but keep a dead product walking?"
So in reality, what people want is "keep focusing on products i care about". But that isn't always a viable model.