The H264 export option seems to be getting phased out with recent updates of Adobe Premiere and After Effects. I do find it odd that H264 has been dropped from the main export menu as it is a widely used format in web and client review outputs. But here is how you can get around it with two simple solutions.
Why is it all changing?
H264 (AVC) is slowly being phased out to make way for the newer H265 High Efficiency Video Coding (HEVC) codec. The newer codec aims to offer a better image quality at smaller file sizes than H264, it also boasts a lower requirement for bandwidth when streaming. With a large majority of video now being accessed by people on mobile devices, often on limited bandwidth it makes total sense to adopt the newer H265 compression.
Should I use H265?
You don’t even need to really change your workflow much to take advantage of it, you just need to know where to find the options. If you decide to use HEVC which is the H265 format, it does not fall under Quicktime anymore, it has its own setting under ‘Format’ and then for your preset you should be able to get away with ‘match source’ in most cases unless you have some specific configurations in mind.
How can I just carry on exporting in H264?
If you want to carry on exporting your videos using H264 then that is still possible using Adobe Media Encoder. Currently After Effects has neither option so you will need to start using Media Encoder to have the options available to you.
Using Media Encoder to export video
It is likely that this is just a move to make the rendering workflow include Media Encoder and get everyone a little more aligned in the way they are using Premiere and After Effects. Its a bit of pain to change a workflow once you become comfortable with it but Its not too much of an overhead to use Media Encoder. Its also not too dissimilar to how Final Cut works with Compressor so the two become more aligned in workflow practices should you ever switch.