At Gen I yes you need a lot less fuel, but remember the equation is exponential a linear reduction in fuel mass causes an almost quadratic reduction in total ship mass.
Lets say at Gen III you would not need a booster rocket just a second stage one.
At lets say Gen V you don't really need high thrust anymore, things like pure ion drives become viable, or thrusters. No need for methalox, or tanks or engines.
At this point space becomes so much cheaper that you ship raw materials and manufacture them in space, you build the satellites in LEO, you build the spaceships in LEO, and if for some reason you need chemical rockets you ship the fuel from earth, that fuel is the fly the cargo not the thing that needs to burn to get there.
Once you get away from the need for high thrust stages you can do almost anything in space, just with transfer orbits and slingshotting you can get almost anywhere in the solar system with enough patience and minimal fuel burn.