It's not about only money and bags. They want control over something that they don't have. Bitcoin is decentralized, and they are trying to get a control over it and make it centralized. Making Bitcoin centralized is impossible, so they took the different approach to take other's coin and put it under control of a centralized platform.
Even if they do it, if people don't use it, they can't control the people. Many will think that, it is controlled by government, so they will get the best security. But then it will have no difference between traditional banks and that exchange platform. It's a well planned move that they are trying to execute. Success is based on public reach and usages. If people refuse to use it, then it will be a very different story. It will be enjoyable to see what will happen.
People using exchanges don't care about their privacy. All they want is a safe exchange that they can use to keep and exchange their funds without restriction. But think I government-owned exchanges can be trusted more than those owned by individuals. My view might not be correct but after the financial recklessness of Bankman-Fried, it became clearer that exchanges controlled by an individual or group of individuals can be easily mismanaged. If the government can guarantee customers that they will receive a refund in case of collapse, then it will be better than other exchanges. But the fact remains clear that keeping money in centralized wallets is at owner's risk, the government and centralized exchanges cannot be trusted.