I understand your frustration. I’m not a Windows and Local user, but I got a windows machine and Installed Local on it. I was able to reproduce the same error (lack of writing permissions on the theme folder).
The error is not a result of a bug in the plugin but the result of the lack of file permissions on the server. If the server doesn’t have permission to write the file, the plugin can’t do anything about this situation; it just warns you about the error. If any plugin or PHP script could change file permissions in the filesystem, the security problems would be massive. The operative system handles the file permissions.
I don’t know this data is up-to-date but, as far as I can read in the Local forums there problem is the following one:
Local uses Docker under the hood to run the sites. What Docker does is load “containers”, a kind of virtual machine, to run the MYSQL and web server (Apache or Nginx) needed to execute WordPress inside it. The problem is that as this entire web environment runs inside the containers, you can’t easily change what happens inside those containers.
Can I change the file permissions of my themes folder using the Windows file explorer? Yes, you can, but those changes will be ignored. Why? When you run Docker the files used by the container are handled by Docker and their own set of user permissions because it is as if it is another machine. You would need to enter the container and modify the file permissions of the folders inside it.
How to connect to the docker instance running the Nginx/apache server and modify the file permissions of the theme folder using Local on Windows? That’s the not easy question we need to solve this problem. I searched for it in the Local forums and didn’t find a good answer.
Meanwhile, what I may suggest is to run WordPress in a different way (not virtualized as with Local/Docker) on your Windows machine.
If something of this needs to be clarified, or you need help with something else, let me know!