I think TikZ rendering would be a great asset to the site. Well-made pictures can be an enormous aid in learning, from diagrams for path integrals in complex analysis to this image illustrating the proof of the Cantor–Schröder–Bernstein Theorem in set theory. Commutative diagrams in particular are essential in areas such as algebra, algebraic geometry, algebraic number theory, and algebraic topology. To my knowledge, the only package for commutative diagrams currently supported by MathJax is amscd, which is very basic and leaves a lot to be desired. (There are already quite a few threads dedicated to finding work-arounds for this limitation: 1, 2, 3.)
To show that there is demand for TikZ rendering, here are some answers that use images generated by TikZ or the commutative diagram package tikz-cd. (Please feel free to add more.)
Here are some to which I might add diagrams if TikZ were supported on the site (and if I were not so lazy).
It's true that I can create an image using TikZ and then upload it, but this is a bit inconvenient (and again, I'm lazy). To do so, I have to:
1) Start my LaTeX editor; 2) Create a new file; 3) Create the image itself; 4) Crop the PDF and save it as a PNG; 5) Upload it to Stack Exchange; 6) Futz around with the size and make sure it looks okay.
Having TikZ support on the site would eliminate all but step 3 (and maybe 6), which would make me much more apt to include pictures in my answers.
In response to quid's comment:
You’re right that in theory steps 1, 2, and 5 take little time. But I’ve been a bit charitable to myself and only included the steps I have to take. Here are all the steps I usually take:
1) Find the TeX file for the most recent image I uploaded to Stack Exchange; 2) Open it and begin modifying it to make a new picture; 3) Realize I forgot to duplicate the file and have instead overwritten it; 4) Duplicate the file and begin modifying it again, while reverting the changes in the old file and recompiling it; 5) Create the new image; 6) Open the PDF in Preview since Adobe Acrobat Reader does not support cropping (the free version available for Mac, anyway); 7) Crop the picture; 8) Try to upload it to Stack Exchange; 9) Realize that although I cropped the image, I forgot to export it as a PNG; 10) Open the image in Preview again and export it as a PNG; 11) Upload the file to Stack Exchange; 12) Futz around with the size and make sure it looks okay.
You might think I’m exaggerating, and it’s true that I don’t make all these mistakes every time I make a picture. But I almost always make at least one (either 3-4 or 8-9).
The resizing part of step 6 of the original list can also be pretty time-consuming. Now that I’ve made a few images, I can finally remember the trick of putting an “m” after the file name to make the picture medium-sized without having to search for one of the meta posts on how to resize images. But sometimes even that doesn’t work well (it didn’t in this one since the figure became too small), and I have to go searching for how to set the picture dimensions exactly using HTML.