The most efficient propeller is single bladed, has infinitely narrow chord, has infinitely thin airfoil, has an infinitely long blade, spins infinitely slowly, and requires infinite torque. So at the risk of stating the obvious, propeller design is a study of the tradeoffs and compromises required to make something practical. Here's a list of some compromises:
- length: landing gear height (or water depth) restricts how long a blade can be.
- material constraints: thicker airfoils resist forces better. Stronger materials allow for thinner airfoils while still meeting required blade strength
- power-plant constraints: the torque required to spin the propeller should match the motor/engine's efficiency and power curves.
- number of blades: more blades equal more thrust for a same diameter
- increased activity factor (aka blade width): wider blades produce more thrust for the same diameter
- balancing: one prop is very hard to balance without causing lots of drag by the opposing mass.
- vibration: three props give fewer vibrations than two
- sound pollution: smaller props spinning more slowly are more pleasing on the ear
- consumer perception: consumers like to see big blades in their fans, regardless of real-world efficiency and performance.
- density of the fluid:
- dense fluids such as water can cause cavitation, which can quickly damage the propeller. One solution is to change tip shape so as to minimize cavitation likelihood.
- on the opposite scale, with low-density fluids such as air, the blade tip can spin so quickly it stalls.
As it relates to drones
Rotorcraft are a little special, so let's break out by type:
Multirotor drones and helicopters have tons of space compared to boats, and so don't particularly need to restrict their diameter. They choose their rotors based primarily on power-plant performance.
Fixed-wing drones with landing gear obey the same rules as full-scale aircraft. If the prop is going to hit the ground on takeoff it's not very useful!
Fixed-wing drones without landing gear, e.g. hand-launch gliders, can use very large folding propellers. These are chosen similarly to multirotors, where it's about efficient power-plant matching.
As pointed out by @RobinBennett, "You don't want it stalled when the aircraft is stationary, so there's a maximum pitch angle - and that sets the maximum speed. If you want to go faster you need to spin the prop faster, and if you've got a fixed amount of power, you need a smaller prop just to spin it faster."