I think that perhaps you might suffer from an attitude of human exceptionalism. If we are "damaging" the planet, as you have said, our demise would be no great loss. However, i have not predicted the demise of humanity, and certainly not because of sea level rise. If the West Antarctic ice sheet breaks free in one to two centuries, people need to be prepared to deal with it. If they do nothing, nature will deal with them. I have complained about increasing the CO2 levels because that might just accelerate the problem. In addition to what Oralloy has mentioned, the estuary of the Thames and the Medway would be inundated, probably all the way to London. They can protect the city by closing the massive and horribly expensive storm surge gates which were built after the North Sea storm surges in the 1950s, but then London ceases to be a sea port. Much of Kent, Susses, Wiltshire, Hampshire, Dorset and Devon wold be inundated. What are now called the Somerset Levels would probably become what they were a thousand years ago, the Somerset Marshes--if they don't actually become an arm of the Severn Sea. Lots of other problems would arise in the United Kingdom.
Holland would very likely be screwed, although they're the one people in the world who are likely to be able to cope with it. A good deal of the French coast would be flooded, and the beaches of the Riviera would disappear. Flood waters would rush up the Tiber, and Rome could be inundated. Large parts of the Italian coast and the Dalmatian coats would be flooded. Spain and Portugal would probably lose their tourist industry, temporarily, but they're in better shape than many European countries. A good deal of the Baltic coasts are barely above sea level, and this would affect Germany, Sweden, Finland, Russia, Latvia, Estonia, Lithuania and Poland.
Bangladesh would be screwed, and so would much of Indonesia--but rather than continue the catalog, i'll just point out that a billion or more people might lose their homes. Effectively, nothing is being done, while we continue to pump CO2 into the atmosphere. Cars and buses and trucks are a problem, but the real problem is cause by coal- and gas-fired power plants. What this Antarctic event really ought to be is a wake-up call that humanity faces big problems, that the capitalists aren't helping, aren't going to help, and will very likely hinder any efforts which they see as jeopardizing their profits. A century or two is really not that long in human affairs when you consider that we'd have to adjust to dramatic changes, not the least of which will be the flooding of prime farm land at a stage in human history at which we seem to be nearing our agricultural carrying capacity.
There are big changes in human society and economics which will need to be made. But the wealthy, and their lick-spittle, paid political lackeys, the very people who need to be addressing these problems, not only are doing nothing, they're trying to crash along, making as much money as possible before the roof caves in on them. Unfortunately, we're all under that roof. If i were truly as smug and uncaring as you suggested earlier, i'd shrug it off, and would never have posted here. I won't be alive when these things happen.