To run in other races. To make money. The owners are interested in making money. Race horses are an investment, they get a winning career then get bred. What would be phony is to limit the Preakness to only Derby runner and the Belmont to only runners of the previous two. That would be a deliberate construct to try to create a Crown winner. Each race has their rules for entry largely independent of each other, a Crown winner has to beat them all.
Imagine if Golf made it so that only the same players play in all four Majors.