There's something wrong with your setup. The top cap is only to provide bearing preload, and the stem should definitely close tight around the steerer tube.

Could it be that your bike originally came with a quick-adjust stem?

Some bikes have what's basically a thick shim that goes over the steerer tube first, and takes the compression from the preload. Then the stem goes over the shim and clamps down around both shim and steerer in the normal fashion. But with the shim doing the preload, the rider can adjust the stem up/down the whole length of the shim w/o having to worry about the headset adjustment going wrong.