Ponders, I think the government doesn't value the NHS for several political reasons. One, it is always a positive for Labour. The Tories know they will never score highly on 'which party would protect the NHS' (or not as highly as Labour).
Two, it was a Labour invention - the post-war Atlee government. The Tories have long memories and still resent the fact that a socialist idea is popular and embedded in our national consciousness. Three, Tories are (since Thatcher) in favour of privatisation and the 'free' market (usually rigged, but whatever) and the NHS directly contradicts that. They would rather have private companies competing to commission and provide healthcare - and indeed their Health Act enables that to happen.
America has the most expensive healthcare in the world yet some of the poorest health outcomes. Their system is mad. There are all sorts of ways different players can manipulate the system to generate profits - doctors ordering unnecessary (and sometimes dangerous/painful) tests, drug companies ramping up prices, the endless bureaucracy caused by having to work out who pays who for what, insurance companies gaming the system by excluding stuff that should be covered, or dropping people once they develop something expensive.
Expat is right about bankruptcy - medical bills are the biggest cause of bankruptcy in the US. European brain surgeons tell me if you develop a glioblastoma tumour in the US, you will go bankrupt. And that's just the financial cost, God knows what the human cost is - but avoidable mortality is significant.