"And yes, if you cut funding to the public funded organisation, then yes private will overtake."
and why wouldn't you want that?
An innovator starts a company with a new or improved idea, the capital markets(us) fund it if we think it's a good idea, the company then succeeds or fails based on whether it can sell it's goods or continue to raise money from us. Put a failed company in public hands and it will continue to bleed the taxpayer for much longer because it's very easy for govt to keep spending taxpayer money with no care about the return. Do this and you quickly end up with a failed state, like all those soviet countries, Cuba, Venezuela etc
Socialism is about protecting failures(people and companies) at the expense of winners. Do enough of this and you kill off winners before they can even start to fund the failures and everyone loses everything ... as your parents know all too well
