Sure, it makes things more convenient. Convenience and security are always a trade-off.

The parent comment was probably asking about some specific advantages.

Convenience is a specific advantage. It also is a great boon when you are used to working in multiple terminals or are running a lot of remote sudo commands over ssh (say testing an ansible setup).

If I set this option, I wonder if OS X third-party app installers will be affected? They often ask for the admin password, presumably to install software in directories owned by the system.

The "advantage" is the convenience mentioned in the (short, succinct) article: I can enter my password for sudo in one terminal window, and escape having to type it again in the other terminal window(s).

I can imagine that some scripts which go deep into the system like e.g. driver installation in OS X might not work anymore after patching OS X yourself.

Are you suggeting that changing documented settings for a system component is "patching OS X yourself"?

Anecdotally, I ran OS X for years with timestamp_timeout set to 0 so that sudo always prompted for a password. This broke absolutely nothing.

Accidentally downvoted you (instead of upvoting).