This is most likely a result of having a Video, or Audio Clip, that "covers" that section, so that Delete and Close Gap will not function.
Can you confirm that - anything above on the Video Tracks, or on the Audio Tracks in that area?
As we await further details from you, I would ask "Have you selected the clips on one side as a group and then just used the mouse cursor to move the group over to meet up with the other half?"
a. You can draw a rectangle around the clips to select them. Once selected the mouse cursor can be used to move them as a group as long as they remain selected in the move.
b. If the Timeline contents tend to get messed up when you are moving clips around on the Timeline, hold down the Alt Key of the computer main keyboard as you move the clips to/around the Timeline.
As Hunt suggests, it sounds like you have content on the upper tracks which often prevent the use of Delete and Close Gap.
If the issue IS something (Video, or Audio) that "covers" that gap, then I completely agree with you. A "lasso" of the necessary Clips, to the right of the gap, then a drag, would be my workflow.
Of course, there ARE some other considerations, like the Duration of any music/soundtrack, when Video Clips are removed, but those can be handled later.