Why is cache_render very big?
It seems like this could be related to particular blocks or other renderable objects on your site that may have many permutations. In one case, I saw 100,000+ rows for one particular views exposed filter block.

Since users were able to select many different options, the block was stored hundreds of times per page/URL in the cache_render table.

It's best to try to scan through the cid values of the table and see any patterns, e.g. with SELECT COUNT(*) FROM cache_render WHERE cid LIKE "%interesting_cid_here%";, to see if there are any major offenders.

Still trying to figure out the best way (besides periodically running drush cr) to fix this issue. For now, I opened up an issue in the Drupal Core issue queue: cache_render table becomes extremely large over time

See discussion around this issue in this Drupal Core issue: Make CACHE_PERMANENT configurable in the database cache — currently allows unlimited growth: cache DB tables of gigabytes!.