Using a wakesurf specific rope is suggested for many reasons we will touch on, but SAFETY is the biggest one.
A normal ski or wakeboard boat has a very wide handle, this is a problem when you wakesurf because as the rope takes slack or you fall it can be easy to get one of your limbs stuck in the handle and then be dragged by the rope.
Surf specific ropes have a much smaller handle or sometimes they have only a knot to hold onto.
Typical ski and wakeboard ropes are very thin, this can be especially dangerous when surfing. When the surfer falls they can be tangled in the rope, thin rope will dig into the human body and can cause a number of serious injuries. The other issue with these ropes is that once you get up and surfing you will want to pull yourself into the "pocket", to do this you will actually be pulling yourself up the rope. Especially in beginners this part of surfing will involve a lot of jerking with the boat and sliding up and back on the wave, with a thin rope in your hand rope burns can be a serious problem. When using thin ropes to avoid the rope burn it can be really tempting to wrap the rope around your hand, which is INCREDIBLE dangerous if you fall you can be dragged or worse.
Surf specific ropes will use a thicker rope as the main line and often have an internal weaved rope, braided section, or soft grips going over the rope. These things all add to the width of the rope making the risk of, and severity of, potential injuries much less. All of these things also make the rope more comfortable.
When the surfer pulls themself into the pocket with a nice thick rope, it is much more comfortable on the hands and with the added grip slipping and rope burns will be almost non-existent.
Ski and wakeboard ropes tend to be very long, sometimes in upwards of 75 feet, this extra length is not needed for surfing and can pose some serious dangers. The longer the rope the more slack there will be as the surfer pulls themself into the pocket, making falls more dangerous with more rope to get caught in.
Wakesurfing ropes are generally 20 to 25 feet in length which give you plenty of space to get up and into the pocket without a ton of excess. You will often see these ropes with removable sections if you find the rope too long to make it even safer and allow for moving around in the pocket with the comfort of the handle and comfortable section at the perfect distance from the boat.
Ski and wakeboard ropes come in tons of sizes, gauges, and materials, but they do not always float. With the rope not staying at the surface the risk of getting the rope stuck in the prop or impeller is much greater. This is dangerous for the boat and potentially incredibly dangerous if there is a combination accident involving the rider stuck in the rope and the rope in the prop.
Using a rope that floats is incredibly beneficial for the rider to keep track of it while they are getting situated in the water. It's also makes it less likely to get caught in the prop causing some real damage.