Update
I was thinking about this.
To be clear, my goal was to be able to type {{cite}} in the source editor, but have the template page name be Template:Citation needed
That way when people are using the visual editor and are browsing templates, it shows up as "Citation needed" (makes sense) instead of "Cite" (sort of abstract, and unless you've edited wikis before), but it's still short and easy to type in the source editor (which experienced users might use).
Though I realised that in both source editors, when you type "{{" it brings up a list templates that match the text as you type.
So it's a little unnecessary with the nice auto-complete list it brings up.
However, you can still have the best of both worlds by using what 452 suggested:
452 wrote:
What is the purpose of substing it? Why not simply use {{Cite}}?
Instead of having the content of Template:Cite be {{needs Citation}}, you could alternately have the contents be #REDIRECT [[Template:needs Citation]], which would ensure that anyone viewing the template would land on the real template page instead of editing the shortcut.
Thanks for suggesting this; I think this is the solution I was looking for. (Though still trying to understand the other one.)
(Despite our different opinions when it comes to design, I do appreciate your help. It'd be much harder to have to work all this stuff out by myself. And I do try to do that as much as I can, anyway.)