They just weren't good enough, ultimately.

Zeppelins have a few key disadvantages in air travel. They're very much more subject to the weather than planes. They are much more expensive to build. They require much more significant ground stations than planes (such as large hangars) for storage and maintenance. They aren't very fast. And they are indeed occasionally hazardous.

A small airplane can be built on a shoestring budget and yet still result in a capable craft that can be operated safely. Building a zeppelin on a shoestring budget will either yield a toy incapable of transporting anyone anywhere or a death trap. Zeppelins are big, and they need to be extraordinarily light, which requires a lot of specialized materials and expensive construction. Going back to the points above, zeppelins are expensive to produce and can require expensive facilities, they represent a very large capital investment. That limits the number of folks who can operate them, it also makes the R&D feedback loop slower and costlier than planes.

You can see the pace of airplane innovation accelerate markedly through the 1930s through the entire 20th century. Zeppelin development proceeds much more slowly. While something like the Graf Zeppelin was a vast improvement over earlier generations it wasn't as big a leap as airplane designs had been making. You see planes go from wood and paper in the 1910s to aluminum frames and skins with turbocharged engines and pressurized cabins by the 1940s to swept wings and jet engines by the '50s and so forth.

With a Zeppelin it takes extraordinary talent to be able to fly them well. You need someone who knows the airship, knows the weather, knows the routes, etc. With an airplane it's possible for many people to learn to fly them well and they are much less subject to bad weather than airships. Planes can fly in the rain, they can fly long distances, they land while under power which is more controllable. Airships are much more fragile, which is why so many of them ended up being severely damaged or destroyed in weather related accidents. In the 1930s the US had a fleet of large airships that it flew as floating aircraft carriers. All of them either had extremely close calls during service or crashed. It took a lot more work and a lot more care to get the success rate with airships higher compared to what was necessary with airplanes.

For a while airplanes were not so much superior to airships so Zeppelins still saw a bit of use and popularity, but that began to change around the 1940s. Planes got better to the point that airships couldn't keep up. You could cross entire oceans in one hop at several hundred mph with a cabin that could hold many people and a significant amount of cargo. Zeppelins couldn't compete with that, and their high production and operation costs meant that they really didn't have much of a chance to hold on in niche operations. With the advent of jet travel (e.g. the Comet and 707) further increasing speeds and ranges of plane travel while also lowering operating costs (which is actually the main benefit of jet engines) there was no way for lighter than airships to keep up in practical sense.