I agree in principal, but in practice no such font is widely available. The emoji cheat sheet has emerged because a desire to use emoji exists, but both input and display are not well supported. The solution I propose, albeit imperfect, works today to display emoji input to those who would not otherwise see it.
There is at least one open font (Symbola) with emoji support and I thought Ubuntu had been adding support at some point recently.
More to the point, however, you could take the symbols you would have to create either way and package them as a web font - which would only be downloaded on devices without a better choice - or simply make your JavaScript do a simple search and replace on the Unicode character values to substitute the same HTML markup you'd need either way. Again, you could do a client side detection for this to avoid any overhead on browsers with support.
Adding backticks to the code spans is set in my CSS: http://mwunsch.tumblr.com/post/15836468477/espresso-tutti-co...
It was a stylistic choice to show off the markdown itself.