The book of golden plates (presuming they did exist and we're buried near Palmyra, NY) remain buried until unearthed by a farmer later in the century or a developer in the next. While later than in OTL, the breadth and scope of settlement of the Great Salt Lake region will "look" much the same. Perhaps some other religious group looking for "space of their own" will find the region appealing.
Well, the area where Joseph Smith lived was known as the
"burned over district", so I'm sure another religious movement would've popped up there eventually. You don't even need to get rid of all of the Smith boys (though as a point, the Smith family did have a long history of religious introspection), just don't have Joseph. Or have him be a normal boy.
Presuming the golden plates existed (which I'm flattered that you are giving the benefit of the doubt to in this scenario), a treasure-hunter might have found them (as a side note, Joseph Smith was accused of being a treasure hunter).
The Great Salt Lake area will be a excellent place for any persecuted religion who want an isolated place, though they might find some isolated region in OTL California more appealing.