It should! DNS is mostly public and therefore shouldn't be used to hold non-public information. Everyone (should) know TLS-protected paths are superior for privacy. The secondary issue is they used low-entropy guessable DNS records at that.
The domain-isolation advantages you mention are easily accomplished by using both a unique, high-entropy subdomain and a long unique path, but rach problem should be addressed individually with explicit goals and not just vibed. Also, aggressively rate-limit probers.