Salt water is considered an antiseptic. This means that it is able to preventing the growth of disease-causing microorganisms. In theory, since ocean water = salt water, it shouldn't be a problem to swim in the ocean even with an open wound.
But that's only the case if the ocean was composed of pure salt water. Our oceans have been contaminated by us humans and are quite nasty especially near the shores. The moisture can make the skin around your wound swell up and complicate the healing process. And with an open wound, you have a very high chance of getting some kind of bacterial infection.
Normally when you cut yourself and start to bleed, special blood cells that have the unique property of sticking together are released. By sticking together they form scabs that then seal the wound off from the outside. However when you are swimming in the ocean, this process takes much longer as the blood is continuously washed away.
Not all shores are made of fine sand. Some of them are made of larger pebbles and some are even littered with massive rocks. Once you mix waves with huge rocks, wounds are just a matter of time especially if you aren't swimming with goggles. The closer you are to the shore the easier it is to get hurt. Whilst entering and leaving the water, there will be an area where you can't swim since there are too many rocks close to the surface. The waves can knock you into the rocks or you might kick one whilst swimming.
Whatever the case, if you continue swimming even after receiving a wound, you'll end up with a wound that looks like you sliced some clay since there will just be a slit. No scabbing, no blood, and it just looks really weird. If you continue to swim every single day, the wound will never properly close and will even start to ooze pus. This is a clear sign that the wound has been infected.
The moral of the story is to bring water proof bandaids to the beach. Just try to at least wash the wound with some bottled water to prevent sealing it in with some sand.