Hello and welcome,
I don’t know about bullpens, as we don’t have many that aren’t within the fencing of the field, and thus most likely would be considered part of the field. I don’t think I’ve ever gotten any bullpens to review, so I don’t know how I’d even judge them.
Batting cages are typically considered separate from the fields, as you do practice hitting and/or pitching in them, and they usually aren’t within the field. Most of the batting cages at the youth fields where I live have Wayspots, and some do share a fence with one of the fields, but they aren’t a part of the field of play.
I tend to approve most batting cages, as they do encourage exercise, even getting used when games aren’t happening often, and may also encourage socializing if you have someone working with you. It’s best when nominating to place the location pin in an area where play doesn’t happen, such as the side or entrance, like in the photo below:
You may also be interested in this post on sports fields: Sports Fields