Leaving an open can of food out on the counter all day is a trend that I have seen happening with friends, family, and clients which is a little disturbing.
The short answer is: No it’s not okay.
To explain once you open a can you have exposed the food to bacteria and unless your house is like a walk in refrigerator and is kept at less than 50°F leaving the can out gives the bacteria like salmonella and listeria time grow. Even though they don’t grow that fast, why risk it? Best refrigerate the food which will inhibit the growth of bacteria.
The other thing to consider is that cats like their food fresh and warm. If your cat was living outdoors he would eat his prey right away while it was still warm and fresh. Leaving the open can of food out all day may leave the food warm but definitely not fresh. It gets dry and starts to spoil even though your nose can’t tell. [Note: many cat food recipes has fish in it even if it doesn’t mention it on the front of the can and you know what fish gets like if it sits out on the counter too long] However, your cat’s nose can tell. Cats eat with their noses in a sense. They smell their food before they eat to make sure that it is fresh, warm and has what they need. If it doesn’t smell right your cat may in the end go off his food. Then you think he’s just being finicky and you buy new food and then the same thing happens with the new food because you continue not to refrigerate the open can of food and not warm it up.
So for food safety and freshness refrigerate the open can of food and warm it up before serving and you will have a very happy kitty.