It seems that they don't crack when roots grow under them. From the PI:

Liz Ellis, an arborist with the city's [Seattle] transportation department, championed bringing rubber sidewalks to Seattle after she read they were being tested in Santa Monica, Calif., and other cities.

She was intrigued not by the novelty of it. Nor did she want to give Seattleites a little extra bounce in their step as the winter gloom sets in.

She pointed to a mound in the rubber sidewalk, raised by the roots growing from one of the red maple trees on the shady, lush street of small houses on Eighth Avenue South, between South Rose and South Thistle streets.

Across the street, where the sidewalk is concrete, the growing roots of another tree had already cracked it. "That (sidewalk) was just put in about a year ago," Ellis said.

The rubberized sidewalks are more elastic, so instead of cracking, they stretch, and have to be replaced less often and are cheaper to fix, Ellis said.

[snip]

Dan Joyce, a principal at the Gardena, Calif.-based rubber sidewalk manufacturer Rubbersidewalks Inc., said 80 cities in eight states are trying rubberized sidewalks. Tacoma and Olympia are among them.