As someone who knows nothing about this: what is wrong with icon fonts?
https://0x0.st/oOUq.png (nullprogram.com)
https://0x0.st/oOUb.png (https://developer.android.com/training/basics/firstapp)
As someone has already pointed out, unlike web fonts, SVGs can be used as inline resources.
It's not just icon fonts though, using web fonts themselves can lead to bad design practices.
It's a normal user modifiable choice in the browser. You're just making your webapp much less usable for users who have made that choice. And for no reason, because SVG icons work just fine and are even more flexible. Font icons are basically a hack. They have terrible fallback behavior.