Why is a ship's hull rounded?

Well, it isn't. Usually. (They aren't).

Most ships are designed to bear a maximum load and the best shape for this is a square-sided box. Like you would see a crane barge operating from - the best shape for lifting and bearing loads.

This is the same for most ships, given that most ships are freighters of one type or another except that they also need to move around the globe. So in order to make them hydrodynamically efficient for this roll the 'box' is reshaped, at the front and back. Though their mid-sections are still box-shaped: Or as you put it: 'Flat'.

So in terms of the section - the cross-section - most ships are 'flat'.

Flat sided, flat bottomed. For load bearing. Box-shaped.

Ships that are designed for rolls other than just load bearing will present a compromise on this theme and will, as you say, be more rounded.

Any departure from this 'load bearing' shape and which tends towards a more rounded section will, at the expense of load bearing, be stronger. With the obvious, most extreme example being the submarine. Which ideally is of circular section.

A mid-way example would be an ice-breaker which for a surface ship is of exceptionally rounded section. Ice breakers are, by necessity, both heavy and strong.
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Edit:

Here is an example of the problem with box-shaped mid sections (not strong enough if badly loaded):

A ship is box shaped basically. The corners are rounded off for strength purposes.
Also to more easily disipate the stress level that are generated on straight corners. This helps to prevent cracking and fracturing of the welded joints in these areas.
To take the ship as a whole unit it is whale shaped with the tail forred and the head aft. The rounded corners have little or nothing to do with aerodynamics and or water resistance. Aerodynamics are provided by the pointy end cutting through the water. This allows the water to flow over the box shaped main sections and then flow smoothly across the rounded aft section onto the propeller and rudder.

The bulbous bows that you often see on a ship are an improvement in reducing the resistance to water f;ow forred.

At low speed, a lot of the resistance to movement is drag from water moving over the hull. That's proportional to wetted area, and round shapes have more volume per surface area than square ones, so a round boat will go faster for the same power. So most sailboats are rounded, and rowboats and kayaks etc. They are harder to build than flat shapes, but they perform better.

At higher speeds, most of the resistance is due to wave-making, so shapes that can rise up out of the water and bounce along the surface (plane) are better.

Inflatable boats are rounded because they are basically a collection of balloons glued together.

It helps the ship cut through the water easier, its like aerodynamics for a car.

That said there are flat bottom ships. LHD, LPD, and almost any amphibious Naval ship is flat bottomed.

To keep the fish from bumping their heads. :)

It helps it cut through the water like the windshield of a car is curved. It might not make sense to people who don't sail but it makes sense to sailors. It is pretty much for speed :)