A similar question was asked 2 years ago, but the best answer was that devices couldn't render vectors fast enough. Most can in 2016, yet there are so few spaces in which I can use those nice .svg files exported from Adobe. Creating resposive sites and emails, it would really help. What is the hold up?
Most current browsers and devices can. However, we still need to support legacy browsers and devices for some time, at least for some projects. We're getting there, but it's a slow process.
I would say that its not the actual support of SVG, but rather the way SVG itself is designed and implemented. On top of this there is the fact that by switching over to a higher abstraction level brings you new problems.
So SVG is a bit broken by design. First there are a lot of features in SVG that you don't actually need in 90% of cases. This slows down the implementation. This resulted in SVG missing the point in time where it would have been easiest to fit into the workflow. Quite simply SVG didn't succeed in its original marketing camping, by the time it was viable it was no longer exciting. Besides web fonts succeed in many ways in the same arena as SVG, but with less problems.
Second broken dimension is that SVG does not really have a sane DOM. So application builders have a extra convolution on top of SVG. Lot of the functionality you would wish is there just is not, and especially earlier was not, available if you link a SVG to a HTML file. This and the nature of SVG as a XML file makes SVG hard to wrok as if it were just a image format. Lots of places wont deliver SVG as if it were a image because of this. Like stack overflow does not support SVG because imgur will not support it as its not a self contained format like a PNG.
While there are other broken things in SVG and implementation of it, i will just skip directly to the higher level problems.
Doing vector graphics, especially for SVG, is not a picnic in the park. Your average editor has somewhat haphazard support for SVG. While its fine if you want to do static images that's not true if you want the images to have interactive features. This isnt really a big problem but since the file is not exactly a image, but instead a recipe to one you get into all kinds of problems with rendering the thing (see this but there are many more such problems).
In the end images are easy. But SVG will get its second chance if and when they adopt SVG as a standard for colored fonts.