Let me start by saying that I don't think that there is going to be any one right or wrong answer to this question, but rather that this question will (and should) receive a lot of good opinion-based answers.
Using IP Restrictions Instead of Disabling Access
IMHO, the authentication mode should be left as-is and instead of following Sitecore's documentation at all, what you should do is use IP restrictions to block requests to the entire /sitecore folder from all locations except the IP of the server itself (for sake of the /KeepAlive.aspx, local access and so on), and the IP of the responsible party for maintaining the site (e.g. the development agency, client's IT department, development VPN, etc.).
Troubleshooting issues on CD environments can be a challenge, especially when log4net priorities are raised to make Sitecore only log ERRORS and access to admin pages like the Jobs Viewer and the Show Config are disabled. Moreover, issues on production CD environments tend to be of the highest priority, since they are on production and on the applications that the general public is hitting. By using IP restrictions to block access to all but those specifically authorized for access, you maintain the same level of security and performance while giving yourself more tools and visibility into the application at troubleshooting time.
If You Still Want to Disable Access...
If you do not want to use IP restrictions (due client security policies, or some other reason) and instead want to follow the guide and blanket-disable access to the /sitecore/admin section then my recommendation would be to change the web.config (preferably via a transform, as described by @ChrisAuer in his comment on the OP) to disable both Forms Authentication and Anonymous Access.