The issue isn't engineering, it's the cost and amount of labor. It can be significantly cheaper to tunnel through a mountain range in an almost straight line than to build on top of one. Once you've started digging into the mountain, you just keep digging and building the tunnel. Barring any maintenance and additional surveys, there is little interruption and the overhead costs can be amortized over the entire length. You will have to swap out drilling equipment as you hit different types and densities of rock but you can often go miles without doing so.
To build on top of a mountain range, there is a smaller overhead cost to survey, do an engineering/environmental study, cut earth, and lay down road but you literally have to pay that overhead for every few hundred feet because as the terrain changes, the equipment and other infrastructure you require also changes drastically. To build a highway you have to have strong ground to build on, which is why US freeways largely bob and weave all over the place instead of just going in a straight line, and civil engineers avoid weak ground where soil stabilization will be most expensive. On mountain roads, not only are the options for soil stabilization limited to very labor intensive methods, but you also often have no choice but to take a bad (expensive) route because you have to design safe turns and gradients. The problem isn't that the engineering is harder, there's just a lot more of it to do.
Also, United States property rights are pretty unique as far as Western countries go. To build a tunnel you'd have to get the mineral rights from every single property owner in your path whereas in most European countries, mineral rights are owned by the government. If you're going to compare a Swiss tunnel to any US road projects, you have to account for the massive differences in legal fees and land acquisition because whether you build above or below ground in the US, you have to deal with the property rights of private owners and all of the extra safety/environmental/etc regulations that come as a consequence.