What I am getting at is that there is no difference between carrying the tank with you and sending it ahead of time and meeting up in orbit. It doesn't change the rocket equation. It just splits your rocket into two rockets.
In KSP you can just add more boosters and fuel to your launch vehicle, but in the real life you have to consider economics.
IIRC for a possible Mars or even moon trip, SpaceX will need to refuel in orbit as well.
My favorite example is “asparagus staging”. In a normal rocket “onion staging” is where multiple liquid rockets are wrapped around a center core, and the outside rockets are drained and expended first. This allows greater thrust at takeoff, while ditching weight once you don’t need it. In KSP these outer rockets can be trivially plumbed together to share fuel, so that only 2 rockets are drained at a time. At the end the center core is left fully fueled for continued flight, since only the exterior tanks were drained.
This is mathematically correct and damn near impossible to engineer. The pumping pressures and volumes are just absurd, since every single tank would need external, severable fuel and oxidizer lines capable of feeding a single motor at 100% thrust. There’s a reason why this tends to show up in KSP and not at say, SpaceX.
Really if you want to maximize the tank size & weight you put into space, separating the two is the only way.
To steel man your point, Starship could be looked at as one giant ass tank with a small payload?