Great article, I always like to structure my queries with CTEs and I was (wrongly) assuming it all gets inlined at the end. Sometimes it also gets complicated since these intermediate results can't be easily seen in a SQL editor. I was working on a UI to parse CTE queries and then execute them step by step to show the results of all the CTEs for easier understanding of the query (as part of this project https://github.com/sqg-dev/sqg/)
I think your assumption about inlining is essentially correct. As far as I know postgres was the last major rdbms to have an optimiser fence around CTEs.