Nobody doing critical infrastructure, public or private will be allowed to go under. Look at the privatised rail companies in the UK or the banks in 2008 for examples of this.
Competition and markets definitely do raise standards where that competition is fair and genuine and well regulated. Usually though, privatisation results in state awarded monopolies where little more gets done than before and costs rise because of the need to show a profit or bail out accrued losses because at the end of the day, the infrastructure has to keep running.
Maybe we can create a marketplace for bidding on infrastructure work job by job and maybe, it could be profitable for everyone. I’m not so sure though.