The problem would still exist, for example when you want to multiply colors which is common in lighting calculations - with integers you would need to divide by

The problem would still exist, for example when you want to multiply colors which is common in lighting calculations - with integers you would need to divide by either 255 or 256 after such an operation. Which floats you only need to make that decision when converting to/from float representation, which is part of what makes them convenient.