Sorry FY8 your argument is fundamentally flawed.
If a company goes bust, generally, everyone involved is out of a job.
If the civil screw a project it is one or two that may pay the consequences, or just get moved side ways.
I would open up for tender - bit by bit - the whole of the civil service.
Let’s be honest - most times people would rather go private anyway if they could - and they are not run by the NHS!
Unfortunately your argument is the fundamentally flawed one, let me explain it to you...
In the private sector you are paid, by the customer, for products or services rendered, nice and easy, I pay you, you give me what I pay for with your profit margin already determined.
Now let's take that model to the private sector where the 'customer' isn't paying you for a a product or services rendered, the government is, therefore the government pays you the budget agreed in the contract. Now this is all well and good if those using the services either remains the same or falls compared to the estimate as you've costed for this, let's remember for the purposes of this example that you will be working with narrow margins, or you wouldn't have won the contract.
Now unfortunately in the real world the pesky public do tend to want to use services more and more, with more and more public exponentially wanting to use more of that service. Now what happens when, as it will, your estimated service user numbers exceed those of your budget, which they will, as you've won the contract by being the lowest bidder? Where do you begin to cut the costs so you stay in profit, which was was a fine line anyway, what with you being the lowest bidder?
Do you cut staff, which assuming you're a streamlined super efficient private company will no doubt damage service delivery, or do you cut the actual services leading to potential harm in either case and difficult visits from those nasty CQC types?
Of course there's option c) Go back to the government cap in hand wanting more public money to prop your business up with, which they may give you short term to stop it collapsing, but good luck when the renewal comes around, or they could action the clause in the contract, which will exist, and take it back out of your money losing hands.
You could of course just run it at a loss realising that there's no profit in public service contract management.
That said, everything might be grand, your margins might stand up, people might not want to use the health service, or civil service, as much as they wanted, you might be lucky.