I'm actually doing one site that the client asked me to put parallax backgrounds on some sections.
What I've discover is that having a section with background-attachment: fixed; and background-size: cover; takes a lot amount of scroll speed and performance of the page. When I remove the background-size and attachment everything went again super smooth and fast and I haven't add a single line of Javascript.
Doing a little search and testing on the topic I read that removing either one (attachment or size) improves the performance, also it has to do with the image size. So what I'm about to test is if I resize the images and make it so that with responsive I change the bg image size if it removes the nerf of performance or will use parallax js to make the exact effect.
So, as a quick summary, don't use more than one section with pure CSS as effect of parallax background, and not even once if the image is bigger than 1MB.