As a serious response, they still exist. Picard walked down a lane in "Family" until he ran into his nephew. And we see people walk around the street where Sisko's is
Streets in towns don't count imo, unless you transport building to building you'll need streets to walk on. The lane though is a fair point though, personally I wonder about intercity roads
The only story we have set in the 20th or 21th century are “Return to Tomorrow Tomorrow is Yesterday”, “Future’s End”, “Future’s End, Part II”, “Carpenter Street”, “Tomorrow and Tomorrow and Tomorrow”, PIC season 2, and First Contact. If there are more, they escape me. These stories are all set on Earth. My best assumption would be that after the 21st century is when automobiles got phased out of society. There isn’t really a good reason to show roads when cars aren’t a necessity for travel.
However for whatever reason, as Mariner points out, we still have bridges.
Yeh. I'd imagine at least in urban areas, they'd be reclaimed. In more unpopulated areas, I could see them becoming hiking/biking trails, or maybe just being left intact in some places for the few hobbyist car drivers left. (I mean, Kirk's stepfather owned a Corvette in the Kelvin films, though that had Nokia product placement for some reason. We'll just say that temporal cold war stuff allowed Nokia to last a bit longer and make car accessories, and that this is still a very old stereo.)
Yeah I can't take the JJ universe seriously when they have that kind of product placement. When I like to have fun with world/lore building in star trek. I would say they do leave some of it intact. The same way we have Pioneer settlements like Cades Cove now or Williamsburg for historical purposes. Hell the Whitehouse is just a museum if it survived WW3.