I've worked on plenty of multi-account projects, and never felt a need to use Organizations. So far as I can tell from this, it allows you to attach permissions to roles in multiple sub-accounts - why wouldn't you be able to use CDK for that?
Organizations also consolidates billing, which means you can (potentially) get usage discounts.
There's a lot of reasons to use Organizations, but I really don't want to write an essay. But it allows things such as segregated security accounts, centralized logging, etc. It can help your security posture a bunch.
Interesting! Technically I guess a lot of that is possible with raw CDK (centralized logging would be, for instance, if you created appropriate roles for each of the managed accounts), but it never hurts to have it done for you automatically! Sounds like it provides sensible default templates for things you _could_ roll by hand if you were feeling masochistic :)
Plus, as the sibling comment said, it predated CDK so was probably the only option at the time.
