Re: > you spend most of your fuel getting the rest of your fuel up to mere subsonic velocity
Mongo, you are also missing the point that it is bad by design, because that is good.
Consider a Saturn 5 engine block. It generates a certain amount of thrust if you pump fuel into it fast enough. Imagine that you have a rocket with only 2/3 of the amount of fuel that NASA actually used. It would weigh substantially less and yet have the same thrust. It would therefore accelerate much faster. So why didn't NASA do it this way? Well, they did. Once you've burnt 2/3 of the fuel in a real Saturn 5, you have exactly the rocket I've just described, except that you are now "launching it" from a platform five miles up traveling at Mach 1.
The optimal launch weight of any rocket is "as much as it can lift". In the case of the Saturn 5, at the moment of launch you have a 3500 ton ballerina balancing just above the launch pad on a downward thrust of exactly the same. (In fact, just to be sure that the launch is truly optimal, I think they overfill it slightly and it doesn't start moving until it has burnt off a little fuel. Fortunately, at 5 tons per second, that doesn't take long.)