However, implementing this in practice is non-trivial. Knowing what is "everyday content" versus what is "once a month content".
To add more complexity -- you have these semi-predictable hype-waves especially two peaks in case of most YT videos where a "once-a-month" content becomes an "everyday" content before again becoming a "once-a-month" content. It feels you could specifically optimise for this -- reduce storage costs without sacrificing UX.
Caching is hard but this sounds like an ARC would likely catch this, if it occurs on a small number of videos concurrently.
After that, you can plunge into colder storages and warm things up as you stream. Additionally, if you need longer to 'defrost' things, just cache a few more MB at the front. Cheat a bit by assuming 480p to start with if you need to; even less to store.
Maybe Google holds your content in 7 data centers round the world (~1 per continent for planned maintenance + latency + reduced oceanic fiber usage).
But with old rarely streamed content they might cut that down to just 3.
The question is whether YT is serving up the one (redundantly-backed storage) copy they have of your almost-never-watched video, or whether it's serving it up from one of 1,000+ copies it's made across the globe for currently popular videos.