There is a Linux utility that takes care of all browsers' abuse of your ssd called profile sync daemon, PSD. It's available in the debian repo or [1] for Ubuntu or [2] for source. It uses `overlay` filesystem to direct all writes to ram and only syncs back to disc the deltas every n minutes using rsync. Been using this for years. You can also manually alleviate some of this by setting up a tmpfs and symlink .cache to it.
[1] https://launchpad.net/~graysky/+archive/ubuntu/utils [2] https://github.com/graysky2/profile-sync-daemon
EDIT: Add link, grammar
EDIT2: Add link to source
Searching on Github, this seems to be it. Turns out, there's releases for Arch, Debian, etc. and it's even in the repositories. No need to add a ppa. https://github.com/graysky2/profile-sync-daemon
For Debian and co:
$ apt-cache show profile-sync-daemon
$ sudo apt-get install profile-sync-daemon