Another reason rockets are so inefficient is that the energy stored in the propellants not only has to accellerate the rocket, it also has to accellerate the unconsumed propellants stored in the rocket. The only way to go faster is to carry more propellants, but that makes your gross weight heavier so the fuel has extra work to do...it's a losing proposition, a Law of Diminishing Returns situation.

The final velocity of a rocket in a zero-g field is given by the Rocket Equation:

Vf = K x ln ( Mi / Mf )

where K is a constant dependent on the type of fuel, engines, etc you are using. Engineers can improve on the value of K, but there is not much they can do about the last term: the natural logarithm of the mass ratio (of initial rocket mass Mi to final rocket mass Mf). All they can hope to do is carry more fuel, and build lighter structures to carry it and lighter payloads, i.e., maximize K and Mi/Mf. Another strategy is to use multiple stages, which is really a means of minimizing Mf. A lot of the energy in the fuel goes into heating up the exhaust and in propelling it out the back, only a fraction of the fuel energy (the "dynamical" energy) is left over to push the rocket and unused fuel forward.

An interesting consequence of this is to calculate the mass ratio at which the final kinetic energy of the empty rocket and payload is maximized compared to the dynamical energy available in the fuel. You can increase speed by increasing Mi/Mf, but kinetic energy increases as 1/2 Mf (Vf )^2.

If we set the Mf to unity, the fuel efficiency is given by dividing the final kinetic energy by the fuel mass consumed (extracting and combining all the stray constants).

Dynamical Efficiency = Constant X [ln (Mi)]^2 / (Mi-1)

This equation has a maximum! The point at which the mass ratio is most efficient, that is, the largest amount of dynamical energy goes into final rocket kinetic energy, is at a ratio of 4.92. In other words, a rocket is most energy efficient when the fully-fueled vehicle masses 4.92 times the empty vehicle. For a single-stage rocket, the math tells you you need 3.92 Kg of propellant for every Kg of airframe and payload. The magic ratio is independent of the type of fuel or propulsion system you use, it's what falls out of the math. Plugging this number back into the equation, we find that roughly 65% of the available dynamical energy goes into accelerating the final mission, the rest went into pushing the unburned fuel you needed just to get there. Not only does the structure and tankage needed increase, the fuel mass itself becomes an issue. You can always go faster by carrying more fuel, but you pay a heavy price for it. Sorry...couldn't resist that.

This is in zero-g, I'm afraid the calculation for the optimum ratio in a gravitational field is beyond my mathematical skills.