I run desktop (not mobile) Firefox with an in-memory cache only. My opinion is that on-disk cache with several days (or weeks) old content is almost entirely useless, and that the most beneficial cache use is what you fetch/reuse through a single day of running browser.

Here's how you can "make the switch":

First of all, clear your disk cache entirely. Then, head into "about:config" and change accordingly:

  browser.cache.disk.enable -> false
  browser.cache.disk.smart_size.enabled -> false
  browser.cache.disk_cache_ssl -> false
  browser.cache.offline.enable -> false
  browser.cache.memory.enable -> true
  browser.cache.memory.capacity -> 512000
  browser.privatebrowsing.forceMediaMemoryCache -> true

The number 512000 is in kilobytes. Adjust to preference. Firefox will still do some caching to disk, but these settings stop the most pressing disk writes. You may confirm the change by visiting "about:cache".

“Several gigabytes” for a browser cache is not abnormal, nor “swamping the disk”. Welcome to the web.