No no no. I've heard this excuse before.
It's down to how the contracts are structured and currently (admittedly) it seems they are often structured very badly indeed. Cleaning services are outsourced now and yet you see crap on the floor all the time. Either the contract doesn't adequately reward cleanliness and penalise dirtiness, or someone in the NHS is not doing their job calling the cleaning company to account. Private companies will always seek to minimise costs - to cut corners even - in order to maximise profits. It's what they do and it's a good thing; it's why capitalism - for all its flaws - is the only system we know of that actually works. So to work in a public service context, you have to be very specific about what you are contracting for and what you are not, and the rewards and the penalties. Then it works. Clearly this is the case because the entire private sector outsources all sorts of things. You do not see this level of push back about privatisation anywhere in the private sector! It's simply a lame excuse those ideologically hell bent on 100% state ownership put forward in order to try to muddy the water.
To answer your specific example, Spire would not get to pick and choose what sort of jobs they want. They'd be given a contract to perform say 10,000 hip operations and get paid (in stages) 30 million quid for it. Of course there would have to contractual provision for things it can't do - exceptions. And those would have impact on the level of reward it receives. The details are unimportant for this discussion. The important bit is that privatisation can be made to work and the idea that it cannot work in public services organisation is a complete smoke screen.