Yes, because government run institutions like the Army and the NHS don't work, do they?
Aren't NHS medical workers in a constant state of protest over low wages and bad working conditions? I know the doctor/nurse brain drain from Canada and the UK to the US used to be really bad. I haven't seen what the statistics are recently.
[0] https://www.marketplace.org/story/2024/02/19/uk-nhs-doctor-s...
Neither of those are beacons of either efficiency or performing to standard. In fact both are chronically mismanaged.
You'd actually struggle to pick worse examples.
Is there even a definition of "doesn't work" that exists for you with the NHS? How inefficient and ineffective does it have to be before it's considered "not working"? Because, technically, every healthcare system on the planet has some effect.
Same for the army.