Well, it could have been 8.000 Joomla articles and you'd still get as many cache files in /cache/com_content. The problem is not K2 and it's certainly not your 8.000 items. And having 8000 files does not spike CPU usage. It's other factors that do (e.g. bad or no MySQL tuning on your webhost's side).

The problem here is clearly your webhost.

Joomla offers many built in caching options by default, e.g. store cache files in RAM (via APCu or Memcached) if "lots" of file nodes is your webhost's actual problem. So if you have APCu or Memcached available as cache options in Joomla's Global Configuration (it's now set to "File"), switch to those. Then cache files will be created to RAM and occupy zero disk space. If that's not an option, disable caching overall.

But I would strongly recommend moving to another host. Cause what they told you is ridiculous for modern hosting. Siteground, Bluehost, GoDaddy, InMotion and a gazillion other companies offer much better shared hosting. If you're looking for a VM/VPS, look at Contabo in Germany (low prices, excellent specs).