A larger problem has been that under current laws, the new directors don’t have the power to hire staff. Nearly 37% of the ministry’s workforce is made up of security guards. The lack of art historians, curators or art marketing experts has made it very difficult to address the museums’ chronic weakness in communications, strategy and fundraising, the directors said.

Anna Coliva, director at Rome’s Borghese Gallery, would like to outsource some of the museum’s services such as managing the ticket office or running restaurant services, but she lacks a staffer with experience in organizing a bid. “We can control our own budget now, which is good, but we don’t have a budget director,” she said.

At the Reggia di Caserta [above], halls are dusty, toilets are dirty and the palace’s 18th century garden is in disrepair because of lack of staff. Mr. Felicori is trying to reallocate some of his 230-strong staff to address the problems, but most are security guards and he can’t make new hires.

When the air conditioning at Capodimonte broke last year, the museum became a “steam bath” when a heat wave swept Italy. But the red tape in securing extra funds to repair the air conditioning was so thick that it remained broken until recently, Mr. Bellenger said.