"The Kennedy Center receives an annual federal appropriation in recognition of the Center’s role as the presidential memorial to John F. Kennedy. These funds pay only for the operation and maintenance, and capital repair and restoration of the building and grounds, ensuring that the living memorial to our 35th president remains a vibrant homage to his legacy."

None of the federal money pays for expenses related to the actual programming and operations of the Kennedy Center, it pays for the building and grounds, which has a separate purpose as the federal memorial to JFK and is also used for a variety of public events and educational functions outside of the Center's performance arts programming. The parent comment asked why the government pays for opera (it doesn't, maybe through a modest NEA grant or something), not "Why does the federal government pay for federal monuments and public spaces?"