It's my understanding that the private owner of the Plaza closes it for one day each year to preserve their private venue status. This allows them to place restrictions on the use of the Plaza as a protest site.
The problem in SLC is that the issue is the LDS church and the non-LDS members of the community. To a small, very vocal faction in SLC, no matter what the LDS church does, it is wrong. They will not be satisfied until either there is total public access on the Plaza with all the demonstrator rights, etc, or the Plaza is replaced with the street again.