I\'m wondering why so few modern web sites still use only PNGs for icons (but this assumption is just based my observation). So far I know, main reasons for using PNGs over SVGs
Unless you are showing very simple shapes/designs or specifically need to modify parts of the graphic with the app, there is not a whole lot of incentive to use SVG. You can produce a PNG at twice the original size (for retina displays) and still have the filesize be an order of magnitude smaller - not to mention better coverage for legacy browsers (no need for javascript or polyfills).
I say this as someone who builds UIs with vector graphics. It's an awesome design tool, but for delivery/bandwidth/reach it's hard to top PNG. Just last night I tested out a well known logo. CocaCola.svg was almost 20K. Since it was a solid/flat color I exported as PNG-8 with 12-color palette compression and got it down to 1.6K (!!!) For just a few logos it's not a big deal, but when you have to show 40 of them.. well, you get the picture.
The best part is that you can turn a PNG into a base64 data uri and embed them right in your stylesheet. This is not recommended with SVG - a format which is already famous for performance and compatibility issues, especially on mobile browsers.
In closing I have to say there are strengths and use cases for both, but PNG has blazed a lot more trails and you face less resistance when you go with the current. For those odd cases where SVG does make a better fit, I highly recommend this article and this learning resource
Happy Designing!