It could, but access through these various CNAMEs would not give it stateful cross-site tracking ability, since each would be a different Origin. It would be providing a hosted first-party analytics/ads/whatever service within the storage space of the first party.

Additionally, people who own the sites can use them together via methods like this, while third parties will have a more difficult time. Bravo.

This has been a feature of Adobe Analytics for over a decade. Google Analytics doesn't currently offer this as a feature, but some enterprising individuals have explored how to hack it in after ITP 2.1 was announced.