It's indeed to log you in to multiple Google properties at once. It's not needed for e.g. Gmail (since it's a subdomain under google.com) but YouTube is in its own domain so it has no access to google.com's cookies.

I turned off YouTube for my account using admin.google.com. Doing so causes Google to stop redirecting me to YouTube and back. Of course this also means I'm never logged in while visiting YouTube.

I guess it's the same reason I go through 4 login screens whenever I want to login to my Microsoft account... Legacy

I can confirm: it’s because of the syncing session cookies across domains.

I do believe it works if you block just the youtube.com domain and not *.youtube.com

You already know the reason.

In additional to youtube.com, in many cases, they redirect to many countries specific domain as well (e.g google.co.jp)

Youtube is common enough that they want to login on the same flow

Other than Chrome browsers don't support third party cookies by default.

Perhaps they want to force companies to not block YouTube.