This is how I view it. If you're going to be hosting dozens or hundreds of sites having a consistent platform like this is important even if Claude Code is doing all of the implementation work. It has understood and workable flows for things like content approval, timed releases, etc. All the things people think about when they talk about "managing content" and for the most part organizations still want human in the loop, especially for gated approvals and auditability.
If I'm thinking of building a single one off site, then yeah I'd probably opt to just let CC handle it without worrying about a framework which is overengineered for my current need. That's what I do with most of the personal projects I work on these days. But I do have a skill to build consistency around the parts that should be consistent for everything I host. Like package shape and types of hooks available for deployment. How sites are publicly exposed and DNS management.