Actually, once you're going to support CJKV languages, and especially more than one of those at the same time, the idea of single font for single document just goes out of window. It already is out of window, just you don't notice it unless you have CJKV users or literacy.
The way it has to work is <english> part of sentences must be rendered in an English font</english>, <chinese-simplified>requires own appropriate font inline</chinese-simplified> and <chinese-traditional>part requires another appropriate font, because there are no distinction in the text binary between Simplified Chinese,</chinese-traditional>, <Japanese>and any other Chinese language variants</Japanese>.
What this has to do with emoji is, same is going on with emoji; emoji is own "language", and the way it has to be and it is supported right now is by switching fonts and calling whoever default and/or can supply missing characters in-line and per-character.
Well, maybe the ship still is on domestic waters on CJKV because there are conspicuous reserved areas in Unicode assignments to hold all CsCtJKV(?) symbols separately, but for emojis it has.