I'm not sure how you expect SE to implement this?
The Unicode characters are stored and served back, it is the fonts used that lack support.
SE uses the stock fonts Arial, "Helvetica Neue", Helvetica, sans-serif so it is up to browser and OS maintainers to get their stuff updated. Once they do the new chars will show.
One possible way for SE to be ahead of browser and OS maintainers is to use Web Fonts. That would still be an external dependency (two actually, one for the font content and one for the server the font is hosted on, assuming they don't host the file on SE servers) but those webfonts might have a release schedule ahead of the stock fonts currently used. Using these fonts might have a performance penalty on page load which, if it does, makes it unlikely to be implemented as page speed is a design feature of the sites.