There isn't a cave on every screen, but there is adventure to be found on every screen! The number of secret items/areas/caves from BOTH quests combined IS close enough to fill 1 entire overworld in LOZ, but that's it. 16x8=128 screens.
Combining both quests' all found overworld items, cave entrances, or warp zones, you get 8 total warps, 10 total heart containers, 2 letters, 4 potion locations, 16 dungeons(level 1 in same spot), 5 sword locations(starting sword in the same spot), 8 gambling locations, 20 shops(some contain free items like the braclet), 20 pay-for-repairs, 28 free rupie locations, 2 blue ring locations, 4 fairy locations. If i missed anything then add it to my total of 119 screens that have items. I might have missed some stuff, such as counting the lost woods(you have to take a specific path, so kind of like a secret), or the waterfall climb(up 5 screens). But as you can see, it's pretty close!