- You're more likely to hit aligment/layout issues because you're using a tool designed for text to render pictures
- The character codes used are textual information but have no semantic meaning (this can be addressed by using ligatures or characters in the private unicode range)
- Adding more icons requires regenerating the font
- Using a subset of icons requires regenerating the font
- Font authoring is non-trivial and requires much more specialized tools and knowledge when compared to SVG
- You need to ship the font in various formats (TTF, OTF, WOFF, WOFF2)
- It's not easy to animate icons, or include colors or transparency
- By now SVG support is sufficiently widespread, so the original rationale for using font icons no longer applies
None of these, except maybe the rendering quality, are deal breakers. Workarounds and counterarguments do exist. And SVG does have some disadvantages too (e.g. parsing overhead, filesize, memory consumption)
I personally side with using SVGs currently. As technology progresses, I might definitely reassess my view.
There are a number of tools that will optimize svg files for size like svgo. Output straight from Illustrator, for example, has a lot room for improvement. I also usually end up hand-tweaking for things like removing the full style and doing that in my site's CSS.
What I think is really still needed are more options besides Illustrator for generating svg content. Yes, Inkscape is overall ok but is lacking in setup ease and genera speed.
There a number of programs that are so close to doing what is needed and then won't save or export an svg. Pixelmater, looking at you.
It isn't just bloody-minded fanatics who object to web fonts.
(full disclosure: I am a bloody-minded fanatic and also object to web fonts)
Your argument about desktop apps isn't very good because people can (and do) prevent desktop apps from doing certain things and accessing various stuff, like web cams, the microphone, system directories, the internet, etc. If my text editor breaks because it can't access my webcam, I'd say it's a serious problem.