Sidewalk root heave is a design problem.
It's easy to blame trees for lifting the sidewalk, but big trees grow big roots, and those roots need space that we usually don't provide beneath pavement. Preventative options, like structural soil and subgrade cells are fantastic solutions to prevent root heave, but we also need to find ways to save the trees that are already lifting the sidewalk and would not survive the root pruning required for standard repairs.
Some species grow more of their roots near the surface, like Bigleaf Maples, but nearly every tree is surface rooting to some degree. So, I think it's time to reframe the design problem.
When a mature tree is lifting the sidewalk we can't just think about putting the right tree in the right spot. The only big mature trees we will ever have in our lifetimes are already here. We need to treat sidewalks as sites to design and build the right sidewalks for the trees we've got.