Moving memory management into the OS often makes sense, because the OS has the big cross-application picture, knows the system-wide memory pressure, and most importantly, already manages the memory of applications, by swapping between RAM and disk.

For the same reason, OS X and Android Linux both have systems for OS managed caches, and AFAIK Firefox already uses these: https://bugzilla.mozilla.org/show_bug.cgi?id=748598

The status on mainline Linux is a bit more nebulous (seems Android's ashmem has been upstreamed, but it's not directly usable on GNU/Linux systems?), and other efforts have stranded: https://lwn.net/Articles/602650/

For some more thoughts about memory management on OS level vs. application level, I can recommend this "random outburst" from the designer of the Varnish HTTP cache: https://www.varnish-cache.org/docs/trunk/phk/notes.html