Let me try to factorize this into two questions:
Can we add a new pre-defined close reason?
My understanding is that there are only 3 slots for pre-defined close reasons. These are already taken by: shopping, individual factors, and out-of-scope. It's possible to replace one of these with a more important reason, but I think that's unlikely.
But these pre-defined close reasons are only there for convenience; those are not the only reasons questions can be closed. You can use the "other" option to specify any other reason.
Should we use the custom reason to vote-to-close trivial/minor questions?
I don't believe we have ever achieved a firm policy here. There is one view that if the internet already contains many sites that explain a simple concept, we don't need to rehash the ground here. The alternative view is that our site should be self-contained; if the question is valid, we should answer it once and then we have an internal duplicate target for future.
Beyond that, I suspect it would be difficult to quantify "trivial." Many of the questions here seem trivial to me (to quote one of my favorite comments: "There are so many questions on here like, 'how do I tell someone I don't want to wibble?', and the answer is simply to say, 'Hey Joe, I don't want to wibble'"), and yet go on to incite significant discussions. So my inclination is to leave such matters to the voters. But that's just my opinion; people with the close vote privilege can use it as they see fit, within reason.