- Government provides services because people need services. While shutdown, those services are not being provided.
- Employees are not being paid. People need to be paid to live.
It's kind of like running a restaurant, seeing that you're spending a lot of money on food and staff, and firing all your staff and cancelling all your food orders to "save money and spend it on other stupid stuff". Except if you're a government, you're hurting more than just yourself and your employees.