A surprising number of systems break down if you pause time by passing a 0 time delta, hence why slowing down time is usually the thing that gets done. The alternative (which you imply with your suggestion) is to pass the many paused states down to every system which further complicates their implementation and is a major source of bugs.

The added fact is that many systems still need to continue running, such as audio, video, and input otherwise the program doesn't appear to respond to input and so isn't in a useable state any more.