Why you shouldn't run as root
While other people have pointed out that you shouldn't run images as root, there isn't much information here, or in the docs about why that is.
While it's true that there is a difference between having root access to a container and root access on the host, root access on a container is still very powerful.
Here is a really good article that goes in depth on the difference between the two, and this issue in general:
https://www.redhat.com/en/blog/understanding-root-inside-and-outside-container
The general point is that if there is a malicious process in your container, it can do whatever it wants in the container, from installing packages, uploading data, hijacking resources, you name it, it can do it.
This also makes it easier for a process to break out of the container and gain privileges on the host since there are no safeguards within the container itself.
How and when to run as non-root
What you want to do is run all your installation and file download/copy steps as root (a lot of things need to be installed as root, and in general it's just a better practice for the reasons I outline below). Then, explicitly create a user and grant that user the minimum level of access that they need to run the application. This is done through the use of chmod and chown commands.
Immediately before your ENTRYPOINT or CMD directive, you then add a USER directive to switch to the newly created user. This will ensure that your application runs as a non-root user, and that user will only have access to what you explicitly gave it access to in previous steps.
The general idea is that the user that runs the container should have an absolute minimum of permissions (most of the time the user doesn't need read, write, and execute access to a file). That way, if there is a malicious process in your container, its behavior will be as restricted as possible. This means that you should avoid creating or copying in any files, or installing any packages as that user too, since they would have complete control over any resources they create by default. I've seen comments suggesting otherwise. Ignore them. If you want to be in line with security best practices, you would then have to go back and revoke the user's excess permissions, and that would just be awful and error prone.