I think this is a useful tag
Here are my reasons for making the tag in the first place:
The purpose of tags is to make it easier to find (or ignore) questions involving a specific topic or type of task. The main argument against the tag that I received was that it wouldn't apply to more than maybe ten questions. I disagree.
There are quite a few questions involving infinite output that don't include
infinite output, so trying to search for them conventionally won't work. This makes it seem like there are fewer applicable questions than there likely are (including the original question I tagged with it). It also gives the tag a good use, since finding related questions is difficult.
Infinite output is a much more common type of challenge than, say, box-256, and it's definitely possible that someone could be searching specifically for infinite output challenges. I see no downside to having the tag.