A content management system is worth it when somebody will genuinely use it. If the site changes twice a year, it adds maintenance and risk for very little return.
Ask one question: who is going to log in, how often, and to change what?
If the answer is a person who will genuinely publish posts, add projects, or update listings weekly or monthly, a CMS pays for itself. If the answer is "someone might, occasionally," you're buying overhead.
The software is usually free. What isn't:
That's the real ongoing cost, and it's covered under ongoing updates and edits.
Not a full CMS, and not a site nobody can touch. A small number of editable areas — hours, prices, a featured project, staff — where the parts that change are editable and the rest stays fixed.
You get control over what actually changes without inheriting an entire platform to maintain.
Minimum viable plugins. An update routine that actually happens. Backups including the database, tested at least once. And a hosting setup suited to it — see free hosting included.
Which shape fits your situation overall is the wider question covered in modern frameworks.
Describe what your business needs and you will get an honest read on what would actually help.