No, it doesn't. Maybe for your personal homepage with three hits per month, but even on a low traffic server, static files gave me headaches.
1) When two visitors write to the file at the same time, the data of one of the visitors will be gone. This can be solved by using lock files. This is a topic on its own (what happens when two processes both create a lockfile at the same time?). Also, when there are a lot of writes happening, multiple processes will wait for the lockfiles, creating load on the server and wait times for the visitor.
2) When a file is read during while another process is doing a write, the file is only read partially. There are workarounds for this as well, you can first write to another file and when done, move this other file to the correct file.
As the number of visitor increases or the file size increases, problems will get harder.
Nowadays it's not hard to add a database. Whether it's on your server or in the cloud. It's performant, it works and it will grow with increasing demand.
It's probably easier to set up than a file based solution.
Sometimes what seems to be simple isn't really.