It's been common in government the last decade or so to "privatize" what
government employees once did.  Therefore governments use private firms to
provide food, custodial, and laundry services; university bookstores are
now under contract to companies like Barnes & Noble that pay rent or a
share of gross; governments now increasingly turn to relying on prisons
built and run by private corporations; etc. etc.  But they are beholden to
government for a specified level of service.

The overhead (including personnel matters) of having museum staff do all
work necessary in the museum can indeed be reduced by privatizing certain
aspects of its operation.

I wonder how many museums have been "turned over to the private sector"
entirely, lock stock and barrel.  In 1982, the one I now direct was opened
as a county-owned and funded museum, having been built over two years under
county direction.  The year following, evidently for political reasons or
because of disagreements, its ownership and its staff were turned over to a
non-profit corporation.  The county instead granted the non-profit the same
amount of money it had spent to run the museum itself, but staff lost
government fringe benefits.  Fifteen years later, we are largely on our
own, with a small annual county grant.  I see this kind of transfer as more
than privatization -- from a government point of view, it means getting rid
of the museum.