The same reasons we repaired the Statue of Liberty, or keep up the Lincoln Memorial or the site of the Battle of Waterloo apply. Historical monuments, sites and momentoes are important in keeping the facts of the past in mind, rather than either forgetting the past or mythologizing it. Documents, works of art, and old things of all types tell us about our past, our culture and ourselves. We keep the Declaration of Independance and the Constitution, in part simply to preserve our culture but also so we can guard against claims that they say something they don't. We'd all like to forget about the Nazi death camps, but the sites are memorialized so we won't forget- not to celebrate them, but to guard against a recurrence. I spent half my life living in a plantation house built in 1830, with a log cabin from 1794 in the yard, both of which are now on the National Historic Register because the past is worth remembering.
It could be argued that the cost of keeping up these memorials and buildings and documents could be spent on other things. But would they be better things? If the money spent on restoring and cleaning Leonardo da Vinci's Last Supper had been spent feeding the poor that would have been great, but would it have actually helped end poverty? It would take a lot more money and a concerted effort on the part of humanity to do that, and I'm not sure it's not beyond our capability. One reason to keep the Missouri Memorial is not to celebrate the War, but to remind us how America once united against aggression, and to help us guard against our own militarist impulses. In other words, not to glorify war, but to remember the sacrifice and terror of such a thing.