This is a question which I think the professional network engineers find very basic. But when asked to explain exactly and clearly why we don't need 255 intermediate hops/routers... well, it's rather hard to explain in simple terms.
The best explanation I've ever come up with is to consider the town or city in which you live: Consider a starting point (at some address in the city) and a desired ending point (also in the city.) Next, select a path (a set of directions) to get from the start to the end. (This is NOT how the Internet works.) How many steps are there in your instructions from start to end? ...4, 5, maybe even 8. But you simply will not need 255 steps to get from one place to another. Next, repeat the exercise from your home address to some place (like a famous museum) on the other side of your country. Again, you will find a surprisingly small number of steps are actually needed.
This result comes from concepts in (if I recall correctly) graph theory from mathematics. It is simply the nature of a connected graph where you have nodes and "edges" (the connections between nodes) passing information (packets on the Internet in our case.) Because the Internet is intentionally designed and built so that you can go to a nearby node (router) which then makes a good decision about where to go next, you effectively go "up" just a few hops and soon find your packet on it's way quickly "over" and then a few hops "down" to the destination.
Wikipedia has a great introduction to Graph Theory.