Everything you've said is correct, but Delta-V scales logarithmicly with fuel load - you need to carry the new fuel. So for purpose of discussing altitude (a valid way to look at getting to the moon) the size of the rocket, and the fuel expended, does in fact grow much closer to linearly.
I think I'll go land on Mun and Minmus now...
What I actually started with was comparing Electron to the current bos.space rocket and seeing the relationship was nowhere near linear. The above is the largest component of why I could think of but there is always more than 1 thing going in.