... ...Are you forgetting that the problem is that most of this ice is ABOVE water? If the ice were BELOW water then yes, you would be right. In fact, if this were the case, the sea level would DROP because the water would become denser as it melts (ice is less dense than water because its expanded). Greenland , for example, is ABOVE sea level, and if it melts then the water that's currently frozen ABOVE the sea will melt, go into the sea and raise the water level. Not only this, but it will dilute the salinity of the ocean, and that's very bad.
If you have a bowl of water with a chunk (or even a large ice cube) of ice sticking out, with part of the ice above the liquid water, then yes, when it melts the liquid water level does rise in that bowl.
I believe the ice melts on Mars yearly, then re freezes. Are aren't on Mars, we are on Earth.