You can't remove the road under a city. So that is a non issue. What tends to happen with the Inca is that you have larger mountain ranges so the city could be shielded (at least from one direction, it's more rare to have blobby mountainranges or a tile that is a mountain surrounded only by other mountain tiles) that way until you get a scouter unit with the trailblazer3 promotion to take the city. You still bombard it from range and then just have the scout move in for the kill and take over. As noted the way for other units to get up there is if you have an actual road/railroad network on mountain tiles. Then just just stand next to it and move up into it and once there you can follow the roads. So if you for some reason do have a road network you need to guard the entrances to the network so others can't get up on the mountain without the proper promotions.