Boxing is a very exciting sport. It is literally pure action, and the breaks are often from the boxers attempting to recover their stamina or holding on to survive. Avoiding hits and clinching also are also breaks from the action. The nature of the sport allows only punches, and this is why there is so much striking action. However, this same reason is why boxing is an incomplete martial art.
We also have legs. Adding in kicks adds a new level of complexity. Hand to hand combat is very mental, and having to defend against kicks can throw someone off that isn’t used to kicks. In addition, some kicks are very tricky, and it can be easy to get caught by one.