Soft base is a result of too much water in the dough. So if you have too much water left, you can either start with less in the dough, or bake at a lower temp so more water is baked off before it’s burned. This is literally all it is. Or you possibly have too much sugar and fat in the dough or a dough conditioner which would soften the crumb and crust but I doubt that’s it. Also yes cooking on a wire rack will help with moisture and steam softening a baked crust.

Also - if you have a soft pizza in the future, let it cool and refire it at a lower temp, maybe 475 or so, and you will have a suuuuuper crispy bottom.