Something similar happened to care homes, making many unprofitable and out of business, and arguably contributing to the current social care crisis.
That's right and politicians tend not to think about it.
They focus on giving stuff to the electorate 'free', but fail to recognise that if you are going to do that via the private sector then those organisations have to remain viable, as they are businesses.
The key issue with nurseries (and probably care homes too, although that's not my are) is that they are tightly regulated with a required ratio of staff to children. Given that by far the greatest expense is staff costs, then there is pretty well no flexibility as you cannot become 'more efficient' by reducing costs, because you can't as that would mean increasing staff to children ratio which would be unlawful.
I gather with the increase in numbers of 'free hours' from 15 to 30 a week only about half of nurseries have signed up to provide it. If that continues the policy will fail as parents won't be able to access their 'free' entitlement in practice, rather than in theory.