Well said. The role of the UX Designer is more of a facilitator and general expert in how and when to serve the correct experience to the user.
Another problem with the UX Designer term is how widespread the job descriptions are in the market. Maybe half of the UX Designers I know are doing the work you describe as the work of an UX Designer. The rest are simply just doing visual UI Design, Web Design or similar work that are part of the user experience but should be titled more specific instead of just using “UX Designer” for everyone.
Just my 2 cents.