There are 2 causes of diffraction spikes: 1. The hexagonal mirrors. Trade off is larger mirrors, and the ability to fold the telescope. 2. The struts holding

There are 2 causes of diffraction spikes: 1. The hexagonal mirrors. Trade off is larger mirrors, and the ability to fold the telescope. 2. The struts holding the secondary mirror. Basically can't get rid of this without a very different telescope design. Causes of both are the best design for getting a lot of light into a space telescope's sensors. In practice has less impact on the science than you might think. The diffraction spikes are much fainter than the main image. It's only bright foreground stars - which the James Webb isn't trying to image anyways - that cause visible spikes.