Why do I have a coax splice behind this blank face plate?
It is likely a remnant from either the initial cable-pulling process, or that connected cable is an extension that was used to &quot;move&quot; the coax to that other point in the room that you mentioned.  I would see what happens if you disconnect it - does the coax stop working somewhere else in your house?  That's the surest way to find out what it is used for.
Since it is a connection, having the access box is handy if you ever need to tighten the connection / move the coax port back to this box.  I don't think there is any code requirement on having access in this instance, though, as it's a signal wire (low voltage) - not power. (as always, IANAL)