The problem isn’t public or private, it’s incentives.

If the private company is granted a defacto monopoly, it doesn’t matter that they’re a “private” company, they will have the same incentive and accountability problem.

What we know for certain though: Government taking over something is definitionally a monopoly and 99.99% of government employees are not subject to the accountability mechanism of elections.

Historically, the largest boondoggles of waste have always come from government, given they can legally hold a gun to your head and take 50% of everyones money to fund their “projects.” Private companies can’t take your money by force, unless being given those contracts by government. So again, the the incentive issue fundamentally arises from an entity being entitled to gather assets using violence rather than voluntary exchange.