Of course coastal erosion is caused by wave action. However, the reason it is a problem is because of mangrove deforestation. Over half of the Pacific islands' mangroves have been rapidly destroyed by human development efforts just in the last 20 years.
Mangroves are the natural, first and best line of defense against coastal erosion. They create soil. Without either mangroves or manmade seawalls, it doesn't matter what the sea level is - the coast will erode at an unsustainable rate.
It really grinds my gears that "solving climate change" - the hardest problem to solve - is presented as a panacea for what are really more complex environmental issues which actually happen to have simpler solutions.