Liquids today are a good means of storing energy, especially in portable applications such as automobiles, cell phones or handguns. The best energy storage/release we can hope for is chemically based, and liquid reactants are easy to bring together, and to refill if the process is irreversible and consumes reactants. Solids compete mainly because they are less prone to leaks and more stable in long term storage applications.
In Trek, energy clearly isn't stored in mundane chemical bonds any more, or a hand phaser would need a fuel tank similar to that of a flamethrower. Liquids might still be in use for some reason X, though. But the fluid that powered the shuttle seemed to be consumed in the process - that is, its remaining quantity dictated the remaining level of energy. If phasers can be charged or drained without physical connections (as per "The Galileo Seven" but others as well), then assuming that they use liquid fuel forces us to assume they feature a liquid fuel generator as well... The treknomagical sarium krellide cells make more sense overall, in terms of continuity at least.
One important thing about the shuttle fuel replenishment mystery is that as far as we can tell, Scotty never repaired the leak that cost them their original fuel. Use of phasers seemed to sidestep the leak issue altogether: phaser power was a "substitute fuel supply", not a means of getting more of the usual fuel, and the main power system had to be specially "adapted" to use this substitute fuel.