It kind of could happen with a few caveats. A warm planet would help, because warm air holds more water and the only mechanism for creating waterfalls is evaporation and weather systems. Water doesn't rise, unless it evaporates, then it rises. All the rain in the world is evaporated, risen water.
So you'd need a warm planet with a strong weather system, perhaps a lower gravity planet, half way between Earth and Mars with lower surface gravity, and a more massive atmosphere, which would balance out with the lower gravity to a similar atmospheric pressure. More volume in the atmosphere would assist in more stored atmospheric water vapor.
Lower gravity would allow higher stable plateaus and cliffs and rain would fall slower and rivers flow with less force, causing less erosion. None of these factors in and of themselves is essential, but each helps.
Lower gravity also leads to lower lapse rate, which means the atmosphere loses heat as air rises more slowly. Clouds could rise higher and there could be more of them. More atmosphere, warm air, so more water vapor and more rain to feed the waterfalls.
The 2nd problem is the shape or drop off, from the continent into the ocean. Granite/continental plates is lighter than Basalt rock that makes up most of the crust. Continents essentially float on the Earth's crust like corks in water.
Source of image
Oceanside cliffs do exist, but they're relatively rare, only a small percentage of total coastline. And oceanside waterfalls are even more rare, if they exist at all. That's the real problem, how to create abundant oceanside waterfalls. Rivers tend to flow somewhat steadily into oceans. They rarely fall from above.
But lets say we have a warm planet with abundant granite and high plateau land masses, mostly a couple/few miles above sea level. The weather on the land masses is warm/temperate, so there's enough water vapor and rain. The weather at sea level is balmy/hot, leading to high evaporation rates, formation of clouds which rise, create rain and disappear. Because much of the rain happens at lower elevation, much of the erosion happens there too, leaving high plateau land masses.
The waterfalls would mostly be cloud fed, not river fed. There will never be enough rivers to make entire coastlines of waterfalls. Rivers tend to combine as they flow down hill, they don't spread out, though there can be some spreading right on the coast.
So, basically this, at least, the left part of the diagram, but instead of a mountain, it's a plateau.
So if you stood at the edge of the cliff overlooking the ocean, you'd see clouds below you. You probably wouldn't see the ocean at all and you might (just maybe) hear the flow of water down the cliff below you, but it wouldn't be a traditional waterfall from the land above. It would look more like a continent wide waterfall flowing down the Oceanside cliffs from below.
Its worth noting that we've never seen a planet in another solar-system. So we don't really know what to expect, but many things are possible. Lower or higher gravity, certainly. Thicker or thinner atmospheres, hotter, colder, more water, less water more extreme seasons, due to higher axial tilt, higher winds. There's an enormous range of what might exist on other planets.
An entire coastline of waterfalls is problematic because rivers tend to cause grooves and combine as they flow downhill, so river based waterfalls should be local, not spread out. Glacial melt waterfalls might be more spread out, and maybe you could have a weather system where a glacier forms every winter and melts every summer, but glacial melt waterfalls would be periodic, like a flood, not permanent.
So, as others have said, not really possible, but some adjustments, you can sort of have that.
