How do you propose to distribute the thrust?
The only way to distribute the thrust is to reduce the pressure (so the water takes longer to be spat out of the 'fire end'). And that reduces the energy stored.
Additionally, distributing the thrust means that you have to lift some of your reaction mass (water) - whereas dumping it all in the first 0.1s means that none of it is lifted beyond about 4-5m of the ground. That leads directly to more energy in the rocket.
Yes, the atmosphere is a bit of a pain - I wonder if they can take a water rocket with them to the moon next time - see how well it goes there ;)